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".

 

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Classe di Scienze Matematiche e Naturali