Recently Fourier–Mukai methods have proved to be a valuable tool in the study of the geometry of irregular varieties. The purpose of this paper is to illustrate these ideas by revisiting some basic results. In particular, we show a simpler proof of the Chen–Hacon birational characterization of abelian varieties. We also provide a treatment, along the same lines, of previous work of Ein and Lazarsfeld. We complete the exposition by revisiting further results on theta divisors. Two preliminary sections of background material are included.
Pareschi, G. (2012). Basic results on irregular varieties via Fourier-Mukai methods. In L. Caporaso, J. McKernan, M. Mustata, M. Popa (a cura di), Current developments in algebraic geometry (pp. 379-403). Cambridge University Press.
Basic results on irregular varieties via Fourier-Mukai methods
PARESCHI, GIUSEPPE
2012-01-01
Abstract
Recently Fourier–Mukai methods have proved to be a valuable tool in the study of the geometry of irregular varieties. The purpose of this paper is to illustrate these ideas by revisiting some basic results. In particular, we show a simpler proof of the Chen–Hacon birational characterization of abelian varieties. We also provide a treatment, along the same lines, of previous work of Ein and Lazarsfeld. We complete the exposition by revisiting further results on theta divisors. Two preliminary sections of background material are included.| File | Dimensione | Formato | |
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