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.

## Mathematical Colloquium: Complex tori, abelian varieties and irregular projective varieties

Rita Pardini

Institution:

Università di Pisa

Location:

A-005

Schedule:

Friday, May 12, 2017 - 16:00 to 17:00

Abstract: