SEMINARIO DI MATEMATICA
Mercoledì 19 settembre 2018
ore 15:00
*Scuola Normale Superiore*
Pisa
Aula Mancini
*Roberto Pirisi*
*(University of British Columbia)*
terrà un seminario dal titolo:
*“**Birational geometry and Gabriel's theorem (Joint with J. Calabrese)”*
*Abstract:*
*It is a well-known result by Gabriel that the category of coherent sheaves of a Noetherian scheme X->S contains sufficient information to reconstruct it, or in another words that an isomorphism Coh(Y) -> Coh(X) (as S-linear categories) induces a corresponding isomorphism X -> Y and vice-versa. As a corollary, the group of automorphisms of Coh(X) is a semidirect product of Aut(X) and Pic(X) (note that tensoring by a line bundle induces an isomorphism on coherent sheaves).** In a recent joint work with J.Calabrese, we prove a birational extension of this result, showing that when X is of finite type over a field the geometry of X "up to dimension d or lower" is controlled by the category Coh_{>d}(X) of coherent sheaves modulo those supported in dimension d or lower, and identify the automorphisms of this category as a semidirect product of the automorphisms of X "up to dimension d or lower" with the group of line bundles on X "up to dimension d or lower".*
Tutti gli interessati sono invitati a partecipare.
Classe di Scienze Matematiche e Naturali
Valeria Giuliani Scuola Normale Superiore Servizio alla Didattica e Allievi tel. 050 509260 Piazza dei Cavalieri, 7 56126 Pisa E-mail: valeria.giuliani@sns.it E-mail: classi@sns.it