Vector bundles on a K3 surface

Abstract

A K3 surface is a quaternionic analogue of an elliptic curve from a view point of moduli of vector bundles. We can prove the algebraicity of certain Hodge cycles and a rigidity of curve of genus eleven and gives two kind of descriptions of Fano threefolds as applications. In the final section we discuss a simplified construction of moduli spaces.

Cited by in corpus (18)

• A category of kernels for equivariant factorizations and its implications for Hodge theory
• On correspondences of a K3 surface with itself. IV
• On K3 Correspondences
• CM liftings of K3 surfaces over finite fields and their applications to the Tate conjecture
• Moduli spaces of twisted sheaves on a projective variety
• Equivalences of twisted K3 surfaces
• Every rational Hodge isometry between two K3 surfaces is algebraic
• The abelian fibration on the Hilbert cube of a K3 surface of genus 9
• On the Picard number of K3 surfaces over number fields
• Real multiplication on K3 surfaces and Kuga Satake varieties
• Correspondences of a K3 surface with itself via moduli of sheaves. I
• On the Hodge conjecture for products of certain surfaces
• Counterexample to the Hodge Conjecture
• The Hodge conjecture for self-products of certain K3 surfaces
• Parametrization of Sing(Theta) for a Fano 3-fold of genus 7 by moduli of vector bundles
• Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8
• Double covers of Kummer surfaces
• Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups