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Journal articles on the topic 'Abel map'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Deconinck, Bernard, and Matthew S. Patterson. "Computing the Abel map." Physica D: Nonlinear Phenomena 237, no. 24 (2008): 3214–32. http://dx.doi.org/10.1016/j.physd.2008.08.007.

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2

Walker, Mark E. "The morphic Abel–Jacobi map." Compositio Mathematica 143, no. 04 (2007): 909–44. http://dx.doi.org/10.1112/s0010437x07002278.

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3

Braden, H. W., and Yu N. Fedorov. "An extended Abel–Jacobi map." Journal of Geometry and Physics 58, no. 10 (2008): 1346–54. http://dx.doi.org/10.1016/j.geomphys.2008.05.009.

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4

Rink, Norman A. "Vortices and the Abel–Jacobi map." Journal of Geometry and Physics 76 (February 2014): 242–55. http://dx.doi.org/10.1016/j.geomphys.2013.10.017.

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5

Wenchuan Hu. "Generalized Abel-Jacobi map on Lawson homology." American Journal of Mathematics 131, no. 5 (2009): 1241–60. http://dx.doi.org/10.1353/ajm.0.0076.

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6

Nagel, Jan. "The Abel-Jacobi map for complete intersections." Indagationes Mathematicae 8, no. 1 (1997): 95–113. http://dx.doi.org/10.1016/s0019-3577(97)83353-8.

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7

Kerr, Matt, James D. Lewis, and Stefan Müller-Stach. "The Abel–Jacobi map for higher Chow groups." Compositio Mathematica 142, no. 02 (2006): 374–96. http://dx.doi.org/10.1112/s0010437x05001867.

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8

Green, Mark L. "Griffiths' infinitesimal invariant and the Abel-Jacobi map." Journal of Differential Geometry 29, no. 3 (1989): 545–55. http://dx.doi.org/10.4310/jdg/1214443062.

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9

Voisin, Claire. "Some Results on Green's Higher Abel-Jacobi Map." Annals of Mathematics 149, no. 2 (1999): 451. http://dx.doi.org/10.2307/120970.

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10

Kimura, Kenichiro. "Nori’s construction and the second Abel-Jacobi map." Mathematical Research Letters 14, no. 6 (2007): 973–81. http://dx.doi.org/10.4310/mrl.2007.v14.n6.a6.

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11

Baker, Matthew, and Xander Faber. "Metric properties of the tropical Abel–Jacobi map." Journal of Algebraic Combinatorics 33, no. 3 (2010): 349–81. http://dx.doi.org/10.1007/s10801-010-0247-3.

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12

Faucette, William M. "Harmonic volume, symmetric products, and the Abel-Jacobi map." Transactions of the American Mathematical Society 335, no. 1 (1993): 303–27. http://dx.doi.org/10.1090/s0002-9947-1993-1075380-8.

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13

Müller-Stach, Stefan. "Syzygies and the Abel-Jacobi map for cyclic coverings." Manuscripta Mathematica 82, no. 1 (1994): 433–43. http://dx.doi.org/10.1007/bf02567712.

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14

Kerr, Matt, and James D. Lewis. "The Abel–Jacobi map for higher Chow groups, II." Inventiones mathematicae 170, no. 2 (2007): 355–420. http://dx.doi.org/10.1007/s00222-007-0066-x.

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15

de Souza, Aldi Nestor, and Frederico Sercio. "On the Degree-1 Abel Map for Nodal Curves." Bulletin of the Brazilian Mathematical Society, New Series 50, no. 3 (2018): 717–43. http://dx.doi.org/10.1007/s00574-018-00127-8.

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16

Achter, Jeffrey D., Sebastian Casalaina-Martin, and Charles Vial. "DISTINGUISHED MODELS OF INTERMEDIATE JACOBIANS." Journal of the Institute of Mathematics of Jussieu 19, no. 3 (2018): 891–918. http://dx.doi.org/10.1017/s1474748018000245.

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We show that the image of the Abel–Jacobi map admits functorially a model over the field of definition, with the property that the Abel–Jacobi map is equivariant with respect to this model. The cohomology of this abelian variety over the base field is isomorphic as a Galois representation to the deepest part of the coniveau filtration of the cohomology of the projective variety. Moreover, we show that this model over the base field is dominated by the Albanese variety of a product of components of the Hilbert scheme of the projective variety, and thus we answer a question of Mazur. We also rec

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17

Nagy, János, and András Némethi. "The Abel map for surface singularities II. Generic analytic structure." Advances in Mathematics 371 (September 2020): 107268. http://dx.doi.org/10.1016/j.aim.2020.107268.

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18

Dupont, Johan L., and Franz W. Kamber. "A generalization of Abel’s Theorem and the Abel–Jacobi map." Illinois Journal of Mathematics 55, no. 2 (2011): 641–73. http://dx.doi.org/10.1215/ijm/1359762406.

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19

Nagy, János, and András Némethi. "The Abel map for surface singularities I: generalities and examples." Mathematische Annalen 375, no. 3-4 (2019): 1427–87. http://dx.doi.org/10.1007/s00208-019-01873-w.

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20

Cohen, Paul E. "Abel Buell, of Connecticut, Prints America's First Map of the United States, 1784." New England Quarterly 86, no. 3 (2013): 357–97. http://dx.doi.org/10.1162/tneq_a_00294.

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After the Revolutionary War concluded, the United States found itself holding clear title to much of North America. The first American to delineate this vast territory was engraver and counterfeiter Abel Buell, whose “Map of the United States” is a legendary rarity. This article provides an account of the map and gives a history of the seven surviving copies.

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21

Jiang, Zhi. "A Noether-Lefschetz theorem for varieties of r-planes in complete intersections." Nagoya Mathematical Journal 206 (June 2012): 39–66. http://dx.doi.org/10.1017/s0027763000010527.

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22

Jiang, Zhi. "A Noether-Lefschetz theorem for varieties of r-planes in complete intersections." Nagoya Mathematical Journal 206 (June 2012): 39–66. http://dx.doi.org/10.1215/00277630-1548484.

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23

Kass, Jesse, and Kirsten Wickelgren. "An Abel map to the compactified Picard scheme realizes Poincaré duality." Algebraic & Geometric Topology 15, no. 1 (2015): 319–69. http://dx.doi.org/10.2140/agt.2015.15.319.

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24

Chien, Mao-Ting, and Hiroshi Nakazato. "Inverse numerical range and Abel-Jacobi map of Hermitian determinantal representation." Linear Algebra and its Applications 633 (January 2022): 227–43. http://dx.doi.org/10.1016/j.laa.2021.10.015.

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25

Danilova, O. V., and V. A. Krasnov. "The Abel--Jacobi Map for Real Hyperelliptic Surfaces of Genus 3." Mathematical Notes 75, no. 5/6 (2004): 601–7. http://dx.doi.org/10.1023/b:matn.0000030967.77252.59.

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26

Voisin, Claire. "Abel-Jacobi map, integral Hodge classes and decomposition of the diagonal." Journal of Algebraic Geometry 22, no. 1 (2012): 141–74. http://dx.doi.org/10.1090/s1056-3911-2012-00597-9.

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27

Molin, Pascal, and Christian Neurohr. "Computing period matrices and the Abel-Jacobi map of superelliptic curves." Mathematics of Computation 88, no. 316 (2018): 847–88. http://dx.doi.org/10.1090/mcom/3351.

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28

Shioda, Tetsuji. "A note on a theorem of Griffiths on the Abel-Jacobi map." Inventiones Mathematicae 82, no. 3 (1985): 461–65. http://dx.doi.org/10.1007/bf01388865.

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29

Abreu, Alex, and Marco Pacini. "The resolution of the universal Abel map via tropical geometry and applications." Advances in Mathematics 378 (February 2021): 107520. http://dx.doi.org/10.1016/j.aim.2020.107520.

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30

Bogatyrev, A. B. "Image of Abel–Jacobi map for hyperelliptic genus 3 and 4 curves." Journal of Approximation Theory 191 (March 2015): 38–45. http://dx.doi.org/10.1016/j.jat.2014.12.005.

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31

Green, Mark, Phillip Griffiths, and Matt Kerr. "Néron models and limits of Abel–Jacobi mappings." Compositio Mathematica 146, no. 2 (2010): 288–366. http://dx.doi.org/10.1112/s0010437x09004400.

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AbstractWe show that the limit of a one-parameter admissible normal function with no singularities lies in a non-classical sub-object of the limiting intermediate Jacobian. Using this, we construct a Hausdorff slit analytic space, with complex Lie group fibres, which ‘graphs’ such normal functions. For singular normal functions, an extension of the sub-object by a finite group leads to the Néron models. When the normal function comes from geometry, that is, a family of algebraic cycles on a semistably degenerating family of varieties, its limit may be interpreted via the Abel–Jacobi map on mot

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32

Bifet, Emili, Franco Ghione, and Maurizio Letizia. "On the Abel-Jacobi map for divisors of higher rank on a curve." Mathematische Annalen 299, no. 1 (1994): 641–72. http://dx.doi.org/10.1007/bf01459804.

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33

Pacini, Marco. "The resolution of the degree-2 Abel-Jacobi map for nodal curves-I." Mathematische Nachrichten 287, no. 17-18 (2014): 2071–101. http://dx.doi.org/10.1002/mana.201200339.

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34

KUZNETSOV, A., L. MANIVEL, and D. MARKUSHEVICH. "ABEL–JACOBI MAPS FOR HYPERSURFACES AND NONCOMMUTATIVE CALABI–YAU'S." Communications in Contemporary Mathematics 12, no. 03 (2010): 373–416. http://dx.doi.org/10.1142/s021919971000383x.

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It is well known that the Fano scheme of lines on a cubic 4-fold is a symplectic variety. We generalize this fact by constructing a closed (2n - 4)-form on the Fano scheme of lines on a (2n - 2)-dimensional hypersurface Yn of degree n. We provide several definitions of this form — via the Abel–Jacobi map, via Hochschild homology, and via the linkage class — and compute it explicitly for n = 4. In the special case of a Pfaffian hypersurface Yn we show that the Fano scheme is birational to a certain moduli space of sheaves of a (2n - 4)-dimensional Calabi–Yau variety X arising naturally in the c

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35

Arosio, Leandro, and Pavel Gumenyuk. "Valiron and Abel equations for holomorphic self-maps of the polydisc." International Journal of Mathematics 27, no. 04 (2016): 1650034. http://dx.doi.org/10.1142/s0129167x16500348.

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We introduce a notion of hyperbolicity and parabolicity for a holomorphic self-map [Formula: see text] of the polydisc which does not admit fixed points in [Formula: see text]. We generalize to the polydisc two classical one-variable results: we solve the Valiron equation for a hyperbolic [Formula: see text] and the Abel equation for a parabolic nonzero-step [Formula: see text]. This is done by studying the canonical Kobayashi hyperbolic semi-model of [Formula: see text] and by obtaining a normal form for the automorphisms of the polydisc. In the case of the Valiron equation, we also describe

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36

Li, Si, Bong H. Lian, and Shing-Tung Yau. "Picard-Fuchs equations for relative periods and Abel-Jacobi map for Calabi-Yau hypersurfaces." American Journal of Mathematics 134, no. 5 (2012): 1345–84. http://dx.doi.org/10.1353/ajm.2012.0039.

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37

Dick, Bernhard. "MELEXIR: maximum entropy Legendre expanded image reconstruction. A fast and efficient method for the analysis of velocity map imaging or photoelectron imaging data." Physical Chemistry Chemical Physics 21, no. 35 (2019): 19499–512. http://dx.doi.org/10.1039/c9cp03353j.

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The MELEXIR program obtains a Legendre expansion of the 3D velocity distribution from 2D images of ions or photoelectrons. The maximum entropy algorithm avoids inverse Abel transforms, is fast and applicable to low-intensity images.

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38

Welters, Gerald E. "The Brauer group and the second Abel-Jacobi map for 0-cycles on algebraic varieties." Duke Mathematical Journal 117, no. 3 (2003): 447–87. http://dx.doi.org/10.1215/s0012-7094-03-11733-0.

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39

Iliev, A., and D. Markushevich. "The Abel-Jacobi map for cubic threefold and periods of Fano threefolds of degree $14$." Documenta Mathematica 5 (2000): 23–47. http://dx.doi.org/10.4171/dm/74.

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40

Brandt, Madeline, and Martin Ulirsch. "Symmetric powers of algebraic and tropical curves: A non-Archimedean perspective." Transactions of the American Mathematical Society, Series B 9, no. 20 (2022): 586–618. http://dx.doi.org/10.1090/btran/113.

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We show that the non-Archimedean skeleton of the d d -th symmetric power of a smooth projective algebraic curve X X is naturally isomorphic to the d d -th symmetric power of the tropical curve that arises as the non-Archimedean skeleton of X X . The retraction to the skeleton is precisely the specialization map for divisors. Moreover, we show that the process of tropicalization naturally commutes with the diagonal morphisms and the Abel-Jacobi map and we exhibit a faithful tropicalization for symmetric powers of curves. Finally, we prove a version of the Bieri-Groves Theorem that allows us, un

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41

Achter, Jeffrey D., Sebastian Casalaina-Martin, and Charles Vial. "On descending cohomology geometrically." Compositio Mathematica 153, no. 7 (2017): 1446–78. http://dx.doi.org/10.1112/s0010437x17007151.

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In this paper, motivated by a problem posed by Barry Mazur, we show that for smooth projective varieties over the rationals, the odd cohomology groups of degree less than or equal to the dimension can be modeled by the cohomology of an abelian variety, provided the geometric coniveau is maximal. This provides an affirmative answer to Mazur’s question for all uni-ruled threefolds, for instance. Concerning cohomology in degree three, we show that the image of the Abel–Jacobi map admits a distinguished model over the rationals.

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42

Faucette, William M. "Higher Dimensional Harmonic Volume Can be Computed as an Iterated Integral." Canadian Mathematical Bulletin 35, no. 3 (1992): 328–40. http://dx.doi.org/10.4153/cmb-1992-045-3.

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AbstractIn this paper it is shown that the computation of higher dimensional harmonic volume, defined in [1], can be reduced to Harris' computation in the onedimensional case (See [3]), so that higher dimensional harmonic volume may be computed essentially as an iterated integral. We then use this formula to produce a specific smooth curve , namely a specific double cover of the Fermat quartic, so that the image of the second symmetric product of in its Jacobian via the Abel-Jacobi map is algebraically inequivalent to the image of under the group involution on the Jacobian.

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43

Swarnjeet, Kaur, and Singh Harmandeep. "A DESCRIPTIVE REVIEW OF DIFFERENT PENETRATION TESTING TOOLS AND METHODS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 5, no. 3 (2016): 221–26. https://doi.org/10.5281/zenodo.47030.

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The  penetration  testing  is to authenticate  a recently discovered and approachable applications and networks, structure  that  are  vulnerable  to a certainty harm ,expose to danger and security  risk   which could reveal unauthorized  access to resources. Penetration testing is a series of actions or steps to reproduce all methods taken by attackers to obtain a system. A penetration tester is the attested , programmed and effective technique  used  to find the  vulnerabilities   in an  attempt  t

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44

Voineagu, Mircea. "Cylindrical homomorphisms and Lawson homology." Journal of K-Theory 8, no. 1 (2010): 135–68. http://dx.doi.org/10.1017/is010004024jkt108.

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AbstractWe use the cylindrical homomorphism and a geometric construction introduced by J. Lewis to study the Lawson homology groups of certain hypersurfaces X ⊂ ℙn + 1 of degree d ℙ n + 1. As an application, we compute the rational semi-topological K-theory of generic cubics of dimensions 5, 6 and 8 and, using the Bloch-Kato conjecture, we prove Suslin's conjecture for these varieties. Using generic cubic sevenfolds, we show that there are smooth projective varieties such that the lowest nontrivial step in their s-filtration is infinitely generated and undetected by the Abel-Jacobi map.

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45

Stevens, Leonie, and Lynette Russell. "The Dutch East India Company (VOC) Tasman Map and Australia: Competing Interests, Myth Making, and an Australian Icon." Thematic Issue: The Social Lives of Maps, Volume 1 92-93 (August 10, 2022): 72–91. http://dx.doi.org/10.7202/1091245ar.

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The floor of the entrance to the Mitchell Library vestibule, which is part of the State Library of New South Wales, displays a stunning mosaic 1939-1941 reproduction of a seventeenth century map recording Abel Tasman’s two journeys of 1642 and 1644. It charts the west, north and southern coasts of the Australian continent, but is incomplete, thus representing the historical moment between an imagined Terra Australis Incognita, and the final survey of the east coast which presaged British colonisation. The original Tasman map, also held by the Mitchell library and currently undergoing restorati

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46

Mawer, Granville Allen. "The Tasman Map: The Biography of a Map: Abel Tasman, the Dutch East India Company and the First Dutch Discoveries of Australia, by Ian Burnet." Imago Mundi 73, no. 1 (2021): 106–7. http://dx.doi.org/10.1080/03085694.2021.1835371.

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47

Chen, Jinbing. "Quasi-Periodic Solutions to the Mixed Kaup-Newell Hierarchy." Zeitschrift für Naturforschung A 73, no. 7 (2018): 579–93. http://dx.doi.org/10.1515/zna-2018-0069.

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AbstractThe mixed Kaup-Newell (mKN) hierarchy, including the nonholonomic deformation of the KN equation, is obtained in the Lenard scheme. By the nonlinearisation of the Lax pair, the mKN hierarchy is reduced to a family of mixed, finite-dimensional Hamiltonian systems (FDHSs) that separate its temporal and spatial variables. It turns out that the Bargmann map not only gives rise to the finite parametric solutions of the mKN hierarchy but also specifies a finite-dimensional, invariant subspace for the mKN flows. The Abel-Jacobi variables are selected to linearise the mKN flows on the Jacobi v

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48

Geng, Xianguo, and Xin Zeng. "Quasi-periodic solutions of the Belov–Chaltikian lattice hierarchy." Reviews in Mathematical Physics 29, no. 08 (2017): 1750025. http://dx.doi.org/10.1142/s0129055x17500258.

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Utilizing the characteristic polynomial of Lax matrix for the Belov–Chaltikian (BC) lattice hierarchy associated with a [Formula: see text] discrete matrix spectral problem, we introduce a trigonal curve with three infinite points, from which we establish the associated Dubrovin-type equations. The essential properties of the Baker–Akhiezer function and the meromorphic function are discussed, that include their asymptotic behavior near three infinite points on the trigonal curve and the divisor of the meromorphic function. The Abel map is introduced to straighten out the continuous flow and th

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49

GUÀRDIA, J. "EXPLICIT GEOMETRY ON A FAMILY OF CURVES OF GENUS 3." Journal of the London Mathematical Society 64, no. 2 (2001): 299–310. http://dx.doi.org/10.1112/s0024610701002538.

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An explicit geometrical study of the curves[formula here]is presented. These are non-singular curves of genus 3, defined over ℚ(a). By exploiting their symmetries, it is possible to determine most of their geometric invariants, such as their bitangent lines and their period lattice. An explicit description is given of the bijection induced by the Abel–Jacobi map between their bitangent lines and odd 2-torsion points on their jacobian. Finally, three elliptic quotients of these curves are constructed that provide a splitting of their jacobians. In the case of the curve [Cscr ]1±√2, which is iso

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50

de Jeu, Rob, and James D. Lewis. "Beilinson's Hodge Conjecture for Smooth Varieties." Journal of K-Theory 11, no. 2 (2013): 243–82. http://dx.doi.org/10.1017/is013001030jkt212.

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AbstractLet U/ℂ be a smooth quasi-projective variety of dimension d, CHr (U,m) Bloch's higher Chow group, andclr,m: CHr (U,m) ⊗ ℚ → homMHS (ℚ(0), H2r−m (U, ℚ(r)))the cycle class map. Beilinson once conjectured clr,m to be surjective [Be]; however, Jannsen was the first to find a counterexample in the case m = 1 [Ja1]. In this paper we study the image of clr,m in more detail (as well as at the “generic point” of U) in terms of kernels of Abel-Jacobi mappings. When r = m, we deduce from the Bloch-Kato conjecture (now a theorem) various results, in particular that the cokernel of clm,m at the gen

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