On the existence of Fourier-Mukai functors

Rizzardo, Alice ORCID: 0000-0001-8423-6499 (2017) On the existence of Fourier-Mukai functors. MATHEMATISCHE ZEITSCHRIFT, 287 (1-2). pp. 155-179.

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Official URL: http://dx.doi.org/10.1007/s00209-016-1821-8

Abstract

A theorem by Orlov states that any equivalence between the bounded derived categories of coherent sheaves of two smooth projective varieties, X and Y, is isomorphic to a Fourier-Mukai transform with kernel in the bounded derived category of coherent sheaves of the product XxY. In the case of an exact functor which is not necessarily fully faithful, we compute some sheaves that play the role of the cohomology sheaves of the kernel, and that are isomorphic to the latter whenever an isomorphism to a Fourier-Mukai transform exists. We then exhibit a class of functors that are not full or faithful and still satisfy the above result.

Item Type:	Article
Additional Information:	19 pages
Uncontrolled Keywords:	Fourier-Mukai functor, Orlov's theorem
Depositing User:	Symplectic Admin
Date Deposited:	21 Dec 2017 08:34
Last Modified:	19 Jan 2023 06:46
DOI:	10.1007/s00209-016-1821-8
Open Access URL:	http://www.research.ed.ac.uk/portal/en/publication...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3014559