Pure and Applied Mathematics Quarterly
Volume 18 (2022)
Special issue celebrating the work of Herb Clemens
Guest Editor: Ron Donagi
The Fourier–Mukai transform made easy
Pages: 1749 – 1770
We propose a slightly modified definition for the Fourier–Mukai transform (on abelian varieties) that makes it much easier to remember various formulas. As an application, we give short proofs for two important theorems: the characterization of GV-sheaves in terms of vanishing, due to Hacon; and fact that M-regularity implies (continuous) global generation, due to Pareschi and Popa.
Fourier–Mukai transform, abelian variety, GV-sheaf, $m$-regularity
The author was partially supported by grant DMS-1404947 from the National Science Foundation, and by a Centennial Fellowship from the American Mathematical Society.
Received 14 December 2021
Received revised 31 December 2021
Accepted 3 January 2022
Published 25 October 2022