Rank two Fourier-Mukai transforms for K3 Surfaces

作者：Maciocia Antony^*

来源：Journal of Geometry and Physics, 2017, 118: 192-201.

DOI：10.1016/j.geomphys.2017.01.020

• Sheaf moduli spaces
• Simple bundles
• K3 surfaces
• Hilbert schemes
• Fourier-Mukai transforms

We study rank two locally-free Fourier-Mukai transforms on K3 surfaces and show that they come in two distinct types according to whether the determinant of a suitable twist of the kernel is positive or not. We show that a necessary and sufficient condition on the existence of Fourier-Mukai transforms of rank 2 between the derived categories of K3 surfaces X and Y with negative twisted determinant is that Y is isomorphic to X and there must exist a line bundle with no cohomology. We use these results to prove that all reflexive K3 surfaces (including the degenerate ones) admit Fourier-Mukai transforms.

• 出版日期2017-8