Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces

By E. Markman. 2004

87 citations recorded by the source corpus.

Abstract Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. We find generators for the cohomology ring of M , with integral coefficients. When S is simply connected and a universal sheaf E exists over S × M , then its class [ E ] admits a Kunneth decomposition as a class in the tensor product K top 0 ( S ) ⊗ K top 0 ( M ) of the topological K-rings. The generators are the Chern classes of the Kunneth factors of [ E ] in K top 0 ( M ) . The general case is similar.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5245e1268d618e48c1b2769caab7a5c4b30e1261

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

INTEGRAL CONSTRAINTS ON THE MONODROMY GROUP OF THE HYPERKÄHLER RESOLUTION OF A SYMMETRIC PRODUCT OF A K3 SURFACE (2006, methodology): “, in the classical topology. For a triple S, v, H, as above, the class αis always topologically trivial; it maps to 0 in H2(M,F), where Fis the sheaf of continuous complex valued invertible functions [Ma3]. Consequently, Edeﬁnes a class [E] ∈ K(S×M), (15) canonical up to tensorization by the pull-ba”
Kirwan surjectivity for quiver varieties (2016, methodology): “ological arguments allow us to conclude (Section 2) that the Chern classes of the tautological bundles generate the cohomology of M. We emphasize that the overall strategy is not new: see [Nak1] (and [Ma]). The new ingredient here is the particular choice of modular compactiﬁcation M. Hiding behind ”
Prime exceptional divisors on holomorphic symplectic varieties and monodromy reflections (2009, background): “ts ﬁnal form in [Y2]. Over S× MH(v) there exists a universal sheaf F, possibly twisted with respect to a non-trivial Brauer class pulled-back from MH(v). Associated to F is a class [F] in K(S×MH(v)) ([Ma4], Deﬁnition 26). Let πi be the projection from S×MH(v) onto the i-th factor. Assume that (v,v) ”
Lagrangian Fibrations of Holomorphic-Symplectic Varieties of K3[n]-Type (2013, background): “s ﬁnal form in [Y1]. Over S× MH(v) there exists a universal sheaf F, possibly twisted with respect to a non-trivial Brauer class pulled-back from MH(v). Associated to F is a class [F] in K(S× MH(v)) ([Ma2], Deﬁnition 26). Let πibe the projection from S×MH(v) onto the i-th factor. LAGRANGIAN FIBRATIO”
A survey of Torelli and monodromy results for holomorphic-symplectic varieties (2011, background): “ M of H-stable sheaves on a K3 surface Sand Mis of K3[n]-type, as in Example 9.6. Choose a basis {x1,x2,...,x24} of K(S). Let u: K(S) → K(M) be the homomorphism given in equation (9.3). Theorem 9.7. ([Ma4], Theorem 1) The cohomology ring H∗(M,Z) is generated by the Chern classes cj(u(xi)), for 1 ≤ i”
Smith theory and irreducible holomorphic symplectic manifolds (2012, background): “Markman [26] proved that H(X, Z) = 0 and H(X, Z) is torsion-free, and Verbitsky [40] proved that the cup product map Sym(2) H(2)(X, Q) → H(4)(X, Q) is an isomorphism.”
The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces (2010, background): “s ﬁnal form in [Y]. Over S× MH(v) there exists a universal sheaf F, possibly twisted with respect to a non-trivial Brauer class pulled-back from MH(v). Associated to F is a class [F] in K(S×MH(v),Z) ([Ma2], Deﬁnition 26). Let πi be the projection from S× MH(v) onto the i-th factor. Assume that (v,v)”