On the Chow ring of certain algebraic hyper-K\

By Claire Voisin. 2006

107 citations recorded by the source corpus.

We study a generalization of a conjecture made by Beauville on the Chow ring of hyper-K\"ahler algebraic varieties. Namely we prove in a number of cases that polynomial cohomological relations involving only CH^1(X) and the Chern classes of X are satisfied in CH(X). These cases are : punctual Hilbert schemes of a K3 surface S parameterizing subschemes of length n, for n<2b_2(S)_tr+5; Fano varieties of lines in a cubic fourfold.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ecd6fd7e945797c984602482455398ee039b8f8d

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In Geometry and Topology

1. M. Shen
2. Charles Vial
3. Claire Voisin
4. D. Huybrechts
5. Kieran G. O’Grady
6. Ulrike Riess
7. L. Fu
8. A. Beauville

In Mathematical Physics

1. M. Shen
2. Claire Voisin
3. Charles Vial
4. Ulrike Riess
5. D. Huybrechts
6. L. Fu
7. A. Beauville
8. Kieran G. O’Grady

Citations in the corpus

• Chow Rings, Decomposition of the Diagonal, and the Topology of Families (2014, methodology): “In the paper [106], we stated the following more general conjecture concerning the Chow ring of an (irreducible algebraic) hyper-Kähler variety.”
• Motivic hyper-Kähler resolution conjecture, I : Generalized Kummer varieties (2016, background): “Now by functorialities and the base change formula (cf. [32, Theorem 6.2]), we have j∗ ◦ q′∗ ◦ p′∗ ◦ δ′∗(1A[n+1]) = q′′∗ ◦ p′′∗ ◦ δ′′∗ (1A[n+1]), which is a polynomial of big diagonals of A|O(11)|+|O(12)|+|O(13)| by Voisin’s result [60, Proposition 5.6], thus symmetrically distinguished in particula”
• The generalized Franchetta conjecture for some hyper-Kähler varieties, II (2020, background): “Note that by Lemma 2.1 ( v ) , the cycles coming from the ambient space are all tautological: Similar subrings are studied for hyperelliptic curves by Tavakol [Tav14], for K3 surfaces by Voisin [Voi08] and Yin [Yin15a], and for cubic hypersurfaces by Diaz [Dia19].”
• Moduli of sheaves and the Chow group of K3 surfaces (2012, background): “In [25] Voisin introduces the product CH0(V )× CH0(V ) −→ CH0(V (2)) ( ∑ imipi, ∑ j njqj) 7→ ∑ i,j minj(pi, qj) One denotes the product of Z1 and Z2 by Z1 ∗Z2.”
• Lectures on K3 Surfaces (2016, background): “This has been put forward by Beauville in [49] and strengthened and verified in a series of examples by Voisin in [620].”
• On the Chow ring of birational irreducible symplectic varieties (2013, background): “Voisin extends this conjecture to the bigger subalgebra which also includes the Chern classes ci (TX ) (see [30]).”
• Remarks And Questions On Coisotropic Subvarieties and 0-Cycles of Hyper-Kähler Varieties (2015, methodology): “In fact, we describe a parametrization of them which should make accessible for them a number of conjectures made in this paper, [5], or [28], by reduction to the case of the variety of lines of a cubic fourfold.”
• Holomorphic symplectic geometry: a problem list (2010, background): “In [6] and [40] the following conjecture is proposed :”