Wednesday, June 1, 2016, at 11 a.m.

Rita Pardini (Università di Pisa)

will speak on

"Linear systems on irregular varieties "

ABSTRACT: I will report on joint work in progress with M.A. Barja (UPC, Barcelona) and L. Stoppino (Università dell'Insubria, Como - Italy).

Given a generically finite map a:X--> A, where X is a smooth projective variety and A is an abelian variety,  and given a line bundle L on X, we study the linear system |L+P|,  where P is a general element of Pic^{^0}(A). We prove that up to taking base change with a suitable multiplication map A-->A, the
map given by  |L+P| is independent of P  and induces  a factorization of the map a.
When L is the canonical bundle of X, this factorization is a new geometrical object  intrinsically attached to the variety X.

The factorization theorem also allows us to  improve   the known Clifford-Severi and Castelnuovo type numerical inequalities for line bundles on X,  under certain assumptions on the map a:X-->A.
A key tool in these proofs is the introduction of a real function, the continuous rank function, that also allows us  to simplify considerably the proof of   the   general Clifford-Severi inequality.

VENUE: Seminar room (DMG, Sezione di Matematica e Informatica, H2 building, Via A. Valerio 12/1, 3rd floor, room 334