The cup product of the Hilbert scheme for K3 surfaces

By M. Lehn, Christoph Sorger. 2000

48 citations recorded by the source corpus.

To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A^[n] in such a way that for any smooth projective surface X with trivial canonical divisor there is a canonical isomorphism of rings between (H*X)^[n] and the cohomology H*(X^[n]) of the n-th Hilbert scheme of X.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Orbifold cohomology for global quotients (2001, methodology): “ group of permutations of the set {1,...,n}; Sn acts on Y by σ(s)i = sσ(i). We prove that the orbifold cohomology H∗ o([Y/Sn]) is naturally isomorphic up to a degree shifting to H∗(S)[n] as deﬁned in [LS2]. There H∗(S)[n] is also shown, up to additional 14 BARBARA FANTECHI AND LOTHAR GOTTSCHE¨ signs”
Generators of the cohomology ring of moduli spaces of sheaves on symplectic surfaces (2000, methodology): “em 1 and for several remarks improving the exposition. Note: After the completion of this paper, M. Lehn and C. Sorger computed the ring structure of the cohomology of Hilbert schemes for K3 surfaces [LS]. 2 The diagonal in terms of Chern classes of a universalsheaf Let S be a K3 or abelian surface,”
On the monodromy of moduli spaces of sheaves on K3 surfaces II (2003, methodology): “ines the character χ′′ i . ✷ 3.3 The Chern classes of TS[n] One may be able to bound by 2 the order |K| of the kernel K of Mon → Mon2, using further knowledge of the ring structure of H∗(S[n],Q) (see [LS1] for a determination of 16 the ring structure). One may even be able to prove the injectivity o”
Higher genus Gromov–Witten invariants as genus zero invariants of symmetric products (2003, background): “ some other simple properties, are suﬃcient to determine the small quantum cohomology of the symmetric product stack SdX in terms of the small quantum cohomology of X. The construction of Lehn-Sorger [26], (see also Fantechi-Go¨ttsche [15]), which calculates the orbifold cohomology of SdXin terms of”
Cohomology ring of crepant resolutions of orbifolds (2001, unknown): “on Conjecture (CHRC) implies that K3[n],(T4)[n] have isomorphic cohomology ring as the orbifold cohomology rings of K3n/Sn,(T4)n/Sn. The later was proved recently by the beautiful works of Lehn-Sorge [LS], Fantechi-Go¨ttsche [FG] and Uribe [U]. It should be mentioned that (i) LehnSorge, Fantanch-Go¨”
On the Chow ring of certain algebraic hyper-K\ (2006, methodology): “The cohomology ring of the Hilbert scheme of a K3 surface has been computed in [14], [16].”