Description of generalized Albanese varieties by curves

TL;DR

This paper demonstrates that the generalized Albanese variety of a possibly singular projective variety over an algebraically closed field of characteristic zero can be derived from a general curve within the variety, simplifying its computation.

Contribution

It shows that the generalized Albanese variety can be computed from a single general curve, providing a new approach for understanding these varieties in characteristic zero.

Findings

The generalized Albanese variety can be obtained from a general curve in the variety.

An explicit example illustrates the computation method.

Unveils properties of the Albanese of Esnault-Srinivas-Viehweg.

Abstract

Let X be a projective variety over an algebraically closed base field, possibly singular. The aim of this paper is to show that the generalized Albanese variety of Esnault-Srinivas-Viehweg can be computed from one general curve C in X, if the base field is of characteristic 0. We illustrate this by an example, which we also use to unravel some mysterious properties of the Albanese of Esnault-Srinivas-Viehweg.