Fourier-Mukai transform of vector bundles on surfaces to Hilbert scheme

2016/05/20 by Biswas, Indranil, Nagaraj, D. S.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.06229

Abstract

Let S be an irreducible smooth projective surface defined over an algebraically closed field k. For a positive integer d, let \rm Hilb^d(S) be the Hilbert scheme parametrizing the zero-dimensional subschemes of S of length d. For a vector bundle E on S, let \mathcal H(E) \longrightarrow \rm Hilb^d(S) be its Fourier--Mukai transform constructed using the structure sheaf of the universal subscheme of S× \rm Hilb^d(S) as the kernel. We prove that two vector bundles E and F on S are isomorphic if the vector bundles \mathcal H(E) and \mathcal H(F) are isomorphic.

Related

• Hilbert schemes of points on some K3 surfaces and Gieseker stable\n bundles
• Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points
• Fourier-Mukai transforms for elliptic surfaces
• Hilbert schemes of elliptic surfaces: group actions and derived categories
• Fourier-Mukai partners of abelian varieties