SISSA Mathematical Colloquium

[Emanuele Tuillier Illingworth]

Mathematical Colloquium


Friday 12 of May, 4.00-5.00pm room A-005 (note the  room change)

Speaker: Rita Pardini, Universita’ di Pisa

Title: Complex tori, abelian varieties and irregular projective varieties

Abstract:

A complex torus T is a complex variety that is the quotient of a complex 
vector space of dimension n by a discrete subgroup of rank 2n (a 
"lattice"); if T can be realized as a closed subvariety of some complex 
projective space then it is called an abelian variety.A complex 
torus/abelian variety  is  in some sense a linear object, since it has a 
natural group structure and its main  geometric invariants  can be 
explicitly described in terms of the lattice.A  smooth complex 
projective variety  is called *irregular* if admits a non constant map 
  to a complex torus.  I will sketch  the construction of the Albanese 
map  of an irregular variety X, namely of  the  "maximal" map from X to 
a complex torus T, and  discuss some instances of how it  can be used to 
analyze geometrical properties of X.