A remark on Beauville’s splitting property

Laterveer, Robert

doi:10.1007/s00229-017-0951-6

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…This property consists in the injectivity of the cycle-class map when restricted to the sub-algebra generated by classes of divisors. This conjecture of Beauville gave rise to several works in the last years [Voi08,Voi12,Fer11,Fu,Rie,Lat,FLV,SYZ,SY,Yin]. Very recently cf.…”

Section: Equivalent Conjecturesmentioning

confidence: 94%

Density of Noether-Lefschetz loci of polarized irreducible holomorphic symplectic varieties and applications

Mongardi,

Pacienza

2018

Preprint

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In this note we derive from deep results due to Clozel-Ullmo the density of Noether-Lefschetz loci inside the moduli space of marked (polarized) irreducible holomorphic symplectic (IHS) varieties. In particular we obtain the density of Hilbert schemes of points on projective K3 surfaces and of projective generalized Kummer varieties in their moduli spaces. We present applications to the existence of rational curves on projective deformations of such varieties, to the study of relevant cones of divisors, and a refinement of Hassett's result on cubic fourfolds whose Fano variety of lines is isomorphic to a Hilbert scheme of 2 points on a K3 surface. We also discuss Voisin's conjecture on the existence of coisotropic subvarieties on IHS varieties and relate it to a stronger statement on Noether-Lefschetz loci in their moduli spaces.

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Section: Equivalent Conjecturesmentioning

confidence: 94%

Density of Noether-Lefschetz loci of polarized irreducible holomorphic symplectic varieties and applications

Mongardi,

Pacienza

2018

Preprint

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“…A first instance of such an existence result is provided by Theorem 1.2. For a (non-exhaustive) list of works in this research direction, see [Voi08, Fer12, Fu13, Fu15, Huy14, Rie16, Voi15, Lat18, Lin20, Lin16, LP19, Yin15, SV16, MP18, Via17, SYZ20, SY20, FLVS19, OSY19, Voi22].…”

Section: Introductionmentioning

confidence: 99%

Families of rational curves on holomorphic symplectic varieties and applications to 0-cycles

Charles,

Mongardi,

Pacienza

2023

Compositio Math.

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We study families of rational curves on irreducible holomorphic symplectic varieties. We give a necessary and sufficient condition for a sufficiently ample linear system on a holomorphic symplectic variety of $K3^{[n]}$ -type to contain a uniruled divisor covered by rational curves of primitive class. In particular, for any fixed $n$ , we show that there are only finitely many polarization types of holomorphic symplectic variety of $K3^{[n]}$ -type that do not contain such a uniruled divisor. As an application, we provide a generalization of a result due to Beauville–Voisin on the Chow group of $0$ -cycles on such varieties.

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Density of Noether–Lefschetz loci of polarized irreducible holomorphic symplectic varieties and applications

Mongardi,

Pacienza

2023

Kyoto J. Math.

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A remark on Beauville’s splitting property

Cited by 3 publications

References 25 publications

Density of Noether-Lefschetz loci of polarized irreducible holomorphic symplectic varieties and applications

Density of Noether-Lefschetz loci of polarized irreducible holomorphic symplectic varieties and applications

Families of rational curves on holomorphic symplectic varieties and applications to 0-cycles

Density of Noether–Lefschetz loci of polarized irreducible holomorphic symplectic varieties and applications

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