Irreducibility of moduli spaces of vector bundles on K3 surfaces

Kota Yoshioka

Irreducibility of moduli spaces of vector bundles on K3 surfaces

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arxiv math/9907001 v2 pith:ZF4W6CEE submitted 1999-07-01 math.AG

Irreducibility of moduli spaces of vector bundles on K3 surfaces

Kota Yoshioka This is my paper

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keywords spacesmodulicomputationssurfacesapplicationassociatedbundlescharacteristics

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In this paper, we show the moduli spaces of stable sheaves on K3 surfaces are irreducible symplectic manifolds, if the associated Mukai vectors are primitive. More precisely, we show that they are related to the Hilbert scheme of points. We also compute the period of these spaces. As an application of our result, we discuss Montonen-Olive duality in Physics. In particular our computations of Euler characteristics of moduli spaces are compatible with Physical computations by Minahan et al.

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Irreducible symplectic varieties via K3-del Pezzo double covers
math.AG 2026-06 unverdicted novelty 6.0

Constructs irreducible symplectic varieties of dimension 2n (2≤n≤10) with 16≤b2≤24 as non-trivial terminalisations of finite symplectic quotients of Beauville-Mukai systems on very general K3-del Pezzo double covers.