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Journal articles on the topic 'Le groupe de Cremona'

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Published: 4 June 2021
Last updated: 19 February 2022

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1

Blanc, Jérémy. "Sous-Groupes Algébriques du Groupe de Cremona." Transformation Groups 14, no. 2 (January 15, 2009): 249–85. http://dx.doi.org/10.1007/s00031-008-9046-5.

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2

Déserti, Julie. "Groupe de Cremona et dynamique complexe." Comptes Rendus Mathematique 342, no. 12 (June 2006): 893–98. http://dx.doi.org/10.1016/j.crma.2006.04.018.

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3

Déserti, Julie. "Le groupe de Cremona est hopfien." Comptes Rendus Mathematique 344, no. 3 (February 2007): 153–56. http://dx.doi.org/10.1016/j.crma.2006.12.005.

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4

Déserti, Julie. "Sur les sous-groupes nilpotents du groupe de Cremona." Bulletin of the Brazilian Mathematical Society, New Series 38, no. 3 (September 2007): 377–88. http://dx.doi.org/10.1007/s00574-007-0050-5.

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5

Déserti, Julie. "Sur les automorphismes du groupe de Cremona." Compositio Mathematica 142, no. 06 (November 2006): 1459–78. http://dx.doi.org/10.1112/s0010437x06002478.

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6

Déserti, Julie. "Sur les automorphismes du groupe de Cremona." Comptes Rendus Mathematique 342, no. 7 (April 2006): 447–52. http://dx.doi.org/10.1016/j.crma.2006.01.008.

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7

Lonjou, Anne. "Pavage de Voronoï associé au groupe de Cremona." Publicacions Matemàtiques 63 (July 1, 2019): 521–99. http://dx.doi.org/10.5565/publmat6321905.

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8

Lonjou, Anne. "Non simplicité du groupe de Cremona sur tout corps." Annales de l’institut Fourier 66, no. 5 (2016): 2021–46. http://dx.doi.org/10.5802/aif.3056.

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9

Pan, Ivan. "Une remarque sur la g�n�ration du groupe de Cremona." Boletim da Sociedade Brasileira de Matem�tica 30, no. 1 (February 1999): 95–98. http://dx.doi.org/10.1007/bf01235676.

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10

Pan, Ivan. "Sur le sous-groupe de décomposition d'une courbe irrationnelle dans le groupe de cremona du plan." Michigan Mathematical Journal 55, no. 2 (August 2007): 285–98. http://dx.doi.org/10.1307/mmj/1187646995.

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11

Catanese, Fabrizio, Ivan Cheltsov, Julie Déserti, and Yuri Prokhorov. "Subgroups of Cremona Groups." Oberwolfach Reports 15, no. 2 (April 11, 2019): 1685–743. http://dx.doi.org/10.4171/owr/2018/28.

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12

Urech, Christian, and Susanna Zimmermann. "Continuous automorphisms of Cremona groups." International Journal of Mathematics 32, no. 04 (February 27, 2021): 2150019. http://dx.doi.org/10.1142/s0129167x21500191.

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We show that if a group automorphism of a Cremona group of arbitrary rank is also a homeomorphism with respect to either the Zariski or the Euclidean topology, then it is inner up to a field automorphism of the base-field. Moreover, we show that a similar result holds if we consider groups of polynomial automorphisms of affine spaces instead of Cremona groups.
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13

Prokhorov, Yuri, and Constantin Shramov. "Jordan property for Cremona groups." American Journal of Mathematics 138, no. 2 (2016): 403–18. http://dx.doi.org/10.1353/ajm.2016.0017.

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14

Popov, V. L. "Tori in the Cremona groups." Izvestiya: Mathematics 77, no. 4 (August 29, 2013): 742–71. http://dx.doi.org/10.1070/im2013v077n04abeh002659.

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15

Urech, Christian. "On homomorphisms between Cremona groups." Annales de l’institut Fourier 68, no. 1 (2018): 53–100. http://dx.doi.org/10.5802/aif.3151.

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16

Popov, V. L. "Borel subgroups of Cremona groups." Mathematical Notes 102, no. 1-2 (July 2017): 60–67. http://dx.doi.org/10.1134/s0001434617070070.

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17

Blanc, Jérémy. "Groupes de Cremona, connexité et simplicité." Annales scientifiques de l'École normale supérieure 43, no. 2 (2010): 357–64. http://dx.doi.org/10.24033/asens.2123.

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18

Blanc, Jérémy, and Susanna Zimmermann. "Topological simplicity of the Cremona groups." American Journal of Mathematics 140, no. 5 (2018): 1297–309. http://dx.doi.org/10.1353/ajm.2018.0032.

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19

Popov, V. L. "Three plots about the Cremona groups." Izvestiya: Mathematics 83, no. 4 (August 2019): 830–59. http://dx.doi.org/10.1070/im8831.

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20

Blanc, Jérémy, Stéphane Lamy, and Susanna Zimmermann. "Quotients of higher-dimensional Cremona groups." Acta Mathematica 226, no. 2 (2021): 211–318. http://dx.doi.org/10.4310/acta.2021.v226.n2.a1.

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21

Blanc, Jérémy, and Jean-Philippe Furter. "Topologies and structures of the Cremona groups." Annals of Mathematics 178, no. 3 (November 1, 2013): 1173–98. http://dx.doi.org/10.4007/annals.2013.178.3.8.

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22

Cornulier, Yves. "Sofic profile and computability of Cremona groups." Michigan Mathematical Journal 62, no. 4 (December 2013): 823–41. http://dx.doi.org/10.1307/mmj/1387226167.

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23

Popov, V. L. "Subgroups of the Cremona groups: Bass’ problem." Doklady Mathematics 93, no. 3 (May 2016): 307–9. http://dx.doi.org/10.1134/s1064562416030248.

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24

Wright, David. "Two-dimensional Cremona groups acting on simplicial complexes." Transactions of the American Mathematical Society 331, no. 1 (January 1, 1992): 281–300. http://dx.doi.org/10.1090/s0002-9947-1992-1038019-2.

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25

Reichstein, Zinovy. "The Jordan property of Cremona groups and essential dimension." Archiv der Mathematik 111, no. 5 (July 24, 2018): 449–55. http://dx.doi.org/10.1007/s00013-018-1218-5.

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26

Cantat, Serge. "Morphisms between Cremona groups, and characterization of rational varieties." Compositio Mathematica 150, no. 7 (June 25, 2014): 1107–24. http://dx.doi.org/10.1112/s0010437x13007835.

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AbstractWe classify all (abstract) homomorphisms from the group$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\sf PGL}_{r+1}(\mathbf{C})$to the group${\sf Bir}(M)$of birational transformations of a complex projective variety$M$, provided that$r\geq \dim _\mathbf{C}(M)$. As a byproduct, we show that: (i)${\sf Bir}(\mathbb{P}^n_\mathbf{C})$is isomorphic, as an abstract group, to${\sf Bir}(\mathbb{P}^m_\mathbf{C})$if and only if$n=m$; and (ii)$M$is rational if and only if${\sf PGL}_{\dim (M)+1}(\mathbf{C})$embeds as a subgroup of${\sf Bir}(M)$.
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27

TOKUNAGA, Hiro-o. "TWO-DIMENSIONAL VERSAL G-COVERS AND CREMONA EMBEDDINGS OF FINITE GROUPS." Kyushu Journal of Mathematics 60, no. 2 (2006): 439–56. http://dx.doi.org/10.2206/kyushujm.60.439.

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28

Muhammed Uludağ, A. "Fundamental groups of a class of rational cuspidal plane curves." International Journal of Mathematics 27, no. 12 (November 2016): 1650104. http://dx.doi.org/10.1142/s0129167x16501044.

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We compute the presentations of fundamental groups of the complements of a class of rational cuspidal projective plane curves classified by Flenner, Zaidenberg, Fenske and Saito. We use the Zariski–Van Kampen algorithm and exploit the Cremona transformations used in the construction of these curves. We simplify and study the group presentations so obtained and determine if they are abelian, finite or big, i.e. if they contain free non-abelian subgroups. We also study the quotients of these groups to some extent.
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29

Delzant, Thomas, and Pierre Py. "Kähler groups, real hyperbolic spaces and the Cremona group. With an appendix by Serge Cantat." Compositio Mathematica 148, no. 1 (November 30, 2011): 153–84. http://dx.doi.org/10.1112/s0010437x11007068.

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AbstractGeneralizing a classical theorem of Carlson and Toledo, we prove thatanyZariski dense isometric action of a Kähler group on the real hyperbolic space of dimension at least three factors through a homomorphism onto a cocompact discrete subgroup of PSL2(ℝ). We also study actions of Kähler groups on infinite-dimensional real hyperbolic spaces, describe some exotic actions of PSL2(ℝ) on these spaces, and give an application to the study of the Cremona group.
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30

Blanc, Jérémy. "Conjugacy classes of affine automorphisms of and linear automorphisms of ℙn in the Cremona groups." manuscripta mathematica 119, no. 2 (January 23, 2006): 225–41. http://dx.doi.org/10.1007/s00229-005-0617-7.

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31

Ustimenko, Vasyl. "On the Families of Stable Multivariate Transformations of Large Order and Their Cryptographical Applications." Tatra Mountains Mathematical Publications 70, no. 1 (September 26, 2017): 107–17. http://dx.doi.org/10.1515/tmmp-2017-0021.

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Abstract Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces Kn over general commutative ring K of with n increasing order can be used in the key exchange protocols and El Gamal multivariate cryptosystems related to them. We suggest to use high degree of noncommutativity of affine Cremona group and modify multivariate El Gamal algorithm via conjugations of two polynomials of kind gk and g−1 given by key holder (Alice) or giving them as elements of different transformation groups. Recent results on the existence of families of stable transformations of prescribed degree and density and exponential order over finite fields can be used for the implementation of schemes as above with feasible computational complexity.
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32

WILLIAMS, GERALD. "UNIMODULAR INTEGER CIRCULANTS ASSOCIATED WITH TRINOMIALS." International Journal of Number Theory 06, no. 04 (June 2010): 869–76. http://dx.doi.org/10.1142/s1793042110003289.

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The n × n circulant matrix associated with the polynomial [Formula: see text] (with d < n) is the one with first row (a0 ⋯ ad 0 ⋯ 0). The problem as to when such circulants are unimodular arises in the theory of cyclically presented groups and leads to the following question, previously studied by Odoni and Cremona: when is Res (f(t), tn-1) = ±1? We give a complete answer to this question for trinomials f(t) = tm ± tk ± 1. Our main result was conjectured by the author in an earlier paper and (with two exceptions) implies the classification of the finite Cavicchioli–Hegenbarth–Repovš generalized Fibonacci groups, thus giving an almost complete answer to a question of Bardakov and Vesnin.
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33

Kekebus, Stefan. "Exposé Bourbaki 1157 : Boundedness results for singular Fano varieties, and applications to Cremona groups following Birkar and Prokhorov-Shramov." Astérisque 422 (2020): 253–90. http://dx.doi.org/10.24033/ast.1136.

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34

Ustimenko, Vasyl, and Oleksandr Pustovit. "On effective computations in subsemigroups of affine Cremona semigroup and implentations of new postquantum multivariate cryptosystems." Physico-mathematical modelling and informational technologies, no. 32 (July 6, 2021): 27–31. http://dx.doi.org/10.15407/fmmit2021.32.050.

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Multivariate cryptography (MC) together with Latice Based, Hash based, Code based and Superelliptic curves based Cryptographies form list of the main directions of Post Quantum Cryptography.Investigations in the framework of tender of National Institute of Standardisation Technology (the USA) indicates that the potential of classical MC working with nonlinear maps of bounded degree and without the usage of compositions of nonlinear transformation is very restricted. Only special case of Rainbow like Unbalanced Oil and Vinegar digital signatures is remaining for further consideration. The remaining public keys for encryption procedure are not of multivariate. nature. The paper presents large semigroups and groups of transformations of finite affine space of dimension n with the multiple composition property. In these semigroups the composition of n transformations is computable in polynomial time. Constructions of such families are given together with effectively computed homomorphisms between members of the family. These algebraic platforms allow us to define protocols for several generators of subsemigroup of affine Cremona semigroups with several outputs. Security of these protocols rests on the complexity of the word decomposition problem, Finally presented algebraic protocols expanded to cryptosystems of El Gamal type which is not a public key system.
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35

Nakano, Tetsuo. "Regular actions of simple algebraic groups on projective threefolds." Nagoya Mathematical Journal 116 (December 1989): 139–48. http://dx.doi.org/10.1017/s0027763000001732.

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The purpose of this note is to study regular actions of simple algebraic groups on projective threefolds as an application of the theory of algebraic threefolds, especially Mori Theory and the theory of Fano threefolds (cf. Mori [11], Iskovskih [7, 8]). The motivation for this study is as follows. In a series of papers, Umemura, in part jointly with Mukai, has classified maximal connected algebraic subgroups of the Cremona group of three variables and also constructed minimal rational threefolds which correspond to such subgroups (cf. Umemura [16-19], Mukai-Ume-mura [12]). In particular, Umemura and Mukai studied in [12] the SL(2, C)-equivariant smooth projectivization of SL(2, C)/G, where G is a binary icosahedral or octahedral subgroup of SL(2, C). The study of equivariant smooth projectivization of SL(2, C)/G for any finite subgroup G has been completed along their lines in Nakano [14]. The main trick of these studies is the investigation of equivariant contraction maps of extremal rays in the context of Mori Theory [11]. In this note, we apply a similar idea to projective threefolds with a regular action of a simple algebraic group and determine which simple algebraic groups can act regularly and nontrivially on projective threefolds and in which fashion. We also need some standard (but difficult) facts from the theory of Fano threefolds. For the precise statement, see Theorem 1 in the main text. For the proof of this theorem, we need a classification of closed subgroups of simple algebraic groups of codimension 1 and 2, which could be derived easily from the classical work of Dynkin [4]. However, we shall give a geometric proof independent of [4] which leads up directly to the proof of Theorem 1. On the whole, we shall establish by geometric methods the scarcity of closed subgroups of small codimension in simple algebraic groups, which is implied in Dynkin [4].
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36

Toppo, Laura, Wanda Liguigli, Chiara Senti, Gianluca Tomasello, Michele Ghidini, Margherita Ratti, Andrea Botticelli, et al. "Presence of bone metastases(BM) at diagnosis is associated with poor prognosis and coagulation disorders (CD) in patients (pts) with advanced gastric cancer (AGC)." Journal of Clinical Oncology 35, no. 15_suppl (May 20, 2017): e15538-e15538. http://dx.doi.org/10.1200/jco.2017.35.15_suppl.e15538.

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e15538 Background: The presence of BM in AGC is a relatively uncommon finding and has a poor prognosis [Leporini C. 2015]. At diagnosis the presence of BM occurs in approximately 10-15% of pts with AGC.[Park 2011; Silvestris 2013]. Aim of this study is to describe the main features of pts with AGC and BM at diagnosis and the prognostic implications. Methods: A consecutive series of AGC followed at Cremona Oncology Division from November 2004 to Dicember 2016 and included in three consecutive prospective trials [Dalla Chiesa M. 2011; Tomasello G. 2013], were analyzed. All pts were treated with a modified DCF (docetaxel, cisplatin, fluorouracil) given as a dose-dense regimen, every 14 days. We analyzed pts with BM at diagnosis (BMaD) and pts without BMaD. We evaluated baseline clinical and pathological parameters, the presence of coagulation disorders (CD) together with efficacy measures in the two groups. Results:218 pts with AGC were identified (38 with BMaD and 180 without BMaD).Main pts characteristics and results are reported in the Table below. Conclusions: The presence of BM at diagnosis in pts with AGC is not a rare event (21%) and identifies a population with a significantly poorer outcome and a higher incidence of CD, that need a clinical monitoring of coagulation parameters. More efforts are required to understand the reasons of the different prognosis and to find specific treatments to improve the survival. [Table: see text]
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37

Dolgachev, Igor V. "Polar Cremona transformations." Michigan Mathematical Journal 48, no. 1 (2000): 191–202. http://dx.doi.org/10.1307/mmj/1030132714.

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38

Staglianò, Giovanni. "Special cubic Cremona transformations of ℙ6 and ℙ7." Advances in Geometry 19, no. 2 (April 24, 2019): 191–204. http://dx.doi.org/10.1515/advgeom-2018-0001.

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Abstract A famous result of Crauder and Katz (1989) concerns the classification of special Cremona transformations whose base locus has dimension at most two. They also proved that a special Cremona transformation with base locus of dimension three has to be one of the following: 1) a quinto-quintic transformation of ℙ5; 2) a cubo-quintic transformation of ℙ6; or 3) a quadro-quintic transformation of ℙ8. Special Cremona transformations as in Case 1) have been classified by Ein and Shepherd-Barron (1989), while in our previous work (2013), we classified special quadro-quintic Cremona transformations of ℙ8. Here we consider the problem of classifying special cubo-quintic Cremona transformations of ℙ6, concluding the classification of special Cremona transformations whose base locus has dimension three.
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39

Zani, Luciano. "Cremona fascista (1922-1940)." MONDO CONTEMPORANEO, no. 1 (September 2017): 5–67. http://dx.doi.org/10.3280/mon2017-001001.

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40

Ein, Lawrence, and Nicholas Shepherd-Barron. "Some Special Cremona Transformations." American Journal of Mathematics 111, no. 5 (October 1989): 783. http://dx.doi.org/10.2307/2374881.

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41

Hulek, Klaus, Sheldon Katz, and Frank-Olaf Schreyer. "Cremona transformations and syzygies." Mathematische Zeitschrift 209, no. 1 (January 1992): 419–43. http://dx.doi.org/10.1007/bf02570843.

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42

Masquelier-Savatier, Chantal. "En groupe ? De groupe ? Au cœur du groupe ?" Cahiers de Gestalt-thérapie Numéro spécial, no. 2 (2013): 9. http://dx.doi.org/10.3917/cges.ns01.0009.

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43

Masquelier-Savatier, Chantal. "En groupe ? De groupe ? Au cœur du groupe ?" Gestalt Numéro spécial, no. 2 (2013): 9. http://dx.doi.org/10.3917/gest.ns01.0009.

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44

Urech, Christian. "Subgroups of elliptic elements of the Cremona group." Journal für die reine und angewandte Mathematik (Crelles Journal) 2021, no. 770 (January 1, 2021): 27–57. http://dx.doi.org/10.1515/crelle-2020-0008.

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Abstract The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a description of the structure of torsion subgroups. As an application, we prove the Tits alternative for arbitrary subgroups of the Cremona group, generalizing a result of Cantat. We also describe solvable subgroups of the Cremona group and their derived length, refining results from Déserti.
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45

Bennett, Marcus, Andrea Mosconi, and Carlo Torresani. "Il Museo Stradivariano di Cremona." Galpin Society Journal 46 (March 1993): 187. http://dx.doi.org/10.2307/842370.

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46

Crauder, Bruce, and Sheldon Katz. "Cremona Transformations and Hartshorne's Conjecture." American Journal of Mathematics 113, no. 2 (April 1991): 269. http://dx.doi.org/10.2307/2374908.

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47

Costa, Barbara, and Aron Simis. "Cremona maps defined by monomials." Journal of Pure and Applied Algebra 216, no. 1 (January 2012): 202–15. http://dx.doi.org/10.1016/j.jpaa.2011.06.007.

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48

Pan, Ivan. "Les transformations de Cremona stellaires." Proceedings of the American Mathematical Society 129, no. 5 (October 12, 2000): 1257–62. http://dx.doi.org/10.1090/s0002-9939-00-05749-x.

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49

Simis, Aron, and Rafael H. Villarreal. "Combinatorics of Cremona monomial maps." Mathematics of Computation 81, no. 279 (September 1, 2012): 1857–67. http://dx.doi.org/10.1090/s0025-5718-2011-02556-1.

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50

Blanc, Jérémy, and Jean-Philippe Furter. "Length in the Cremona group." Annales Henri Lebesgue 2 (2019): 187–257. http://dx.doi.org/10.5802/ahl.18.

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