Journal of the Ramanujan Mathematical Society

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Fourier-Mukai Transform of Vector Bundles on Surfaces to Hilbert Scheme


Affiliations
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
2 The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India
     

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Let S be an irreducible smooth projective surface defined over an algebraically closed field k. For a positive integer d, let Hilbd (S) be the Hilbert scheme parametrizing the zero-dimensional subschemes of S of length d. For a vector bundle E on S, let H(E) → Hilbd (S) be its Fourier–Mukai transform constructed using the structure sheaf of the universal subscheme of S × Hilbd (S) as the kernel. We prove that two vector bundles E and F on S are isomorphic if the vector bundles H(E) and H(F) are isomorphic.
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  • Fourier-Mukai Transform of Vector Bundles on Surfaces to Hilbert Scheme

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Authors

Indranil Biswas
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
D. S. Nagaraj
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India

Abstract


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