Gotowe bibliografie tematyczne / Fano fourfolds of K3 type

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Gotowa bibliografia na temat „Fano fourfolds of K3 type”

Autor: Grafiati

Data publikacji: 5 października 2024

Data aktualizacji: 31 lipca 2025

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Artykuły w czasopismach na temat "Fano fourfolds of K3 type"

Fu, Lie, Robert Laterveer, and Charles Vial. "Multiplicative Chow–Künneth decompositions and varieties of cohomological K3 type." Annali di Matematica Pura ed Applicata (1923 -) 200, no. 5 (2021): 2085–126. http://dx.doi.org/10.1007/s10231-021-01070-0.

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AbstractGiven a smooth projective variety, a Chow–Künneth decomposition is called multiplicative if it is compatible with the intersection product. Following works of Beauville and Voisin, Shen and Vial conjectured that hyper-Kähler varieties admit a multiplicative Chow–Künneth decomposition. In this paper, based on the mysterious link between Fano varieties with cohomology of K3 type and hyper-Kähler varieties, we ask whether Fano varieties with cohomology of K3 type also admit a multiplicative Chow–Künneth decomposition, and provide evidence by establishing their existence for cubic fourfold

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Laterveer, Robert. "On the Chow ring of certain Fano fourfolds." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 19, no. 1 (2020): 39–52. http://dx.doi.org/10.2478/aupcsm-2020-0004.

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AbstractWe prove that certain Fano fourfolds of K3 type constructed by Fatighenti–Mongardi have a multiplicative Chow–Künneth decomposition. We present some consequences for the Chow ring of these fourfolds.

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Mongardi, Giovanni. "On symplectic automorphisms of hyper-Kähler fourfolds of K3[2] type." Michigan Mathematical Journal 62, no. 3 (2013): 537–50. http://dx.doi.org/10.1307/mmj/1378757887.

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Laza, Radu, and Kieran O’Grady. "Birational geometry of the moduli space of quartic surfaces." Compositio Mathematica 155, no. 9 (2019): 1655–710. http://dx.doi.org/10.1112/s0010437x19007516.

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By work of Looijenga and others, one understands the relationship between Geometric Invariant Theory (GIT) and Baily–Borel compactifications for the moduli spaces of degree-$2$ $K3$ surfaces, cubic fourfolds, and a few other related examples. The similar-looking cases of degree-$4$ $K3$ surfaces and double Eisenbud–Popescu–Walter (EPW) sextics turn out to be much more complicated for arithmetic reasons. In this paper, we refine work of Looijenga in order to handle these cases. Specifically, in analogy with the so-called Hassett–Keel program for the moduli space of curves, we study the variatio

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Tanimoto, Sho, and Anthony Várilly-Alvarado. "Kodaira dimension of moduli of special cubic fourfolds." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 752 (2019): 265–300. http://dx.doi.org/10.1515/crelle-2016-0053.

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Abstract A special cubic fourfold is a smooth hypersurface of degree 3 and dimension 4 that contains a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a countable family of Noether–Lefschetz divisors {{\mathcal{C}}_{d}} in the moduli space {{\mathcal{C}}} of smooth cubic fourfolds. These divisors are irreducible 19-dimensional varieties birational to certain orthogonal modular varieties. We use the “low-weight cusp form trick” of Gritsenko, Hulek, and Sankaran to obtain information about the Kodaira dimension of {{\mathcal{C}}_{d}} . For example, if {d=6

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Pym, Brent. "Elliptic singularities on log symplectic manifolds and Feigin–Odesskii Poisson brackets." Compositio Mathematica 153, no. 4 (2017): 717–44. http://dx.doi.org/10.1112/s0010437x16008174.

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A log symplectic manifold is a complex manifold equipped with a complex symplectic form that has simple poles on a hypersurface. The possible singularities of such a hypersurface are heavily constrained. We introduce the notion of an elliptic point of a log symplectic structure, which is a singular point at which a natural transversality condition involving the modular vector field is satisfied, and we prove a local normal form for such points that involves the simple elliptic surface singularities$\widetilde{E}_{6},\widetilde{E}_{7}$and$\widetilde{E}_{8}$. Our main application is to the class

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Konovalov, V. A. "THE USE OF MARKOV ALGORITHMS FOR THE STUDY OF l-VOIDS IN BIG DATA OF SOCIO-ECONOMIC SYSTEMS. PART 2." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 217 (July 2022): 30–41. http://dx.doi.org/10.14489/vkit.2022.07.pp.030-041.

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The second part of the article is presented. Big data l-voids are considered using the N-scheme of the Markov algorithm. The diagrams of occurrences of l-voids in a semi-Eulerian cycle containing an Euler path, a matroid and an incomplete Fano matroid, minors K3, 3 and K5, an extra large cycle of occurrences are analyzed. An example of reconstructing a fragment of an incomplete Fano matroid with l-voids is considered. Examples are given for independent implementation of the method of filling the artificial intelligence database (AnwM f typeK) DB based on the results of the analysis of l-voids

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Kretschmer, Andreas. "The Chow ring of hyperkähler varieties of $$K3^{[2]}$$-type via Lefschetz actions." Mathematische Zeitschrift, September 9, 2021. http://dx.doi.org/10.1007/s00209-021-02846-z.

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AbstractWe propose an explicit conjectural lift of the Neron–Severi Lie algebra of a hyperkähler variety X of $$K3^{[2]}$$ K 3 [ 2 ] -type to the Chow ring of correspondences $$\mathrm{CH}^*(X \times X)$$ CH ∗ ( X × X ) in terms of a canonical lift of the Beauville–Bogomolov class obtained by Markman. We give evidence for this conjecture in the case of the Hilbert scheme of two points of a K3 surface and in the case of the Fano variety of lines of a very general cubic fourfold. Moreover, we show that the Fourier decomposition of the Chow ring of X of Shen and Vial agrees with the eigenspace de

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Höring, Andreas, and Saverio Andrea Secci. "FANO FOURFOLDS WITH LARGE ANTICANONICAL BASE LOCUS." Journal of the Institute of Mathematics of Jussieu, January 20, 2025, 1–31. https://doi.org/10.1017/s1474748024000604.

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Abstract A famous theorem of Shokurov states that a general anticanonical divisor of a smooth Fano threefold is a smooth K3 surface. This is quite surprising since there are several examples where the base locus of the anticanonical system has codimension two. In this paper, we show that for four-dimensional Fano manifolds the behaviour is completely opposite: if the base locus is a normal surface, and hence has codimension two, all the anticanonical divisors are singular.

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Huybrechts, Daniel. "Chow groups of surfaces of lines in cubic fourfolds." Épijournal de Géométrie Algébrique Special volume in honour of... (July 30, 2023). http://dx.doi.org/10.46298/epiga.2023.10425.

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The surface of lines in a cubic fourfold intersecting a fixed line splits motivically into two parts, one of which resembles a K3 surface. We define the analogue of the Beauville-Voisin class and study the push-forward map to the Fano variety of all lines with respect to the natural splitting of the Bloch-Beilinson filtration introduced by Mingmin Shen and Charles Vial.

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Rozprawy doktorskie na temat "Fano fourfolds of K3 type"

Hernandez, Gomez Jordi Emanuel. "Transformations spéciales des quadriques." Electronic Thesis or Diss., Université de Toulouse (2023-....), 2024. http://www.theses.fr/2024TLSES086.

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Dans cette thèse, nous étudions les transformations birationnelles spéciales des quadriques lisses. Nous obtenons un résultat de classification en dimensions 3 et 4. Dans ces deux cas, nous démontrons qu'il n'existe qu'un seul exemple. Pour la dimension 3, il est défini par le système linéaire de quadriques passant par une courbe rationnelle normale quartique. Pour la dimension 4, il est défini par le système linéaire de cubiques passant par une surface K3 non minimale de degré 10 avec 2 (-1)-droites disjointes qui n'est contenue dans aucune autre quadrique. Le lieu de base de la transformatio

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Części książek na temat "Fano fourfolds of K3 type"

Bolognesi, Michele, and Robert Laterveer. "On the Chow Ring of Fano Fourfolds of K3 Type." In Progress in Mathematics. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-66230-0_14.

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Huybrechts, Daniel. "Hodge Theory of Cubic Fourfolds, Their Fano Varieties, and Associated K3 Categories." In Lecture Notes of the Unione Matematica Italiana. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18638-8_5.

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