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