Severi inequality for varieties of maximal Albanese dimension

TL;DR

This paper proves a Severi inequality for high-dimensional complex varieties of maximal Albanese dimension, relating their canonical volume to their Euler characteristic, extending classical inequalities to a broader class of varieties.

Contribution

It establishes a new inequality linking the canonical volume and Euler characteristic for varieties of maximal Albanese dimension, generalizing previous results to higher dimensions.

Findings

Proves $K_X^n \,\ge\, 2 n! \chi(K_X)$ for the specified varieties.

Extends Severi inequality to higher-dimensional varieties of maximal Albanese dimension.

Provides a fundamental inequality in the classification theory of algebraic varieties.

Abstract

Let $X$ be a projective, normal, minimal and Gorenstein $n$-dimensional complex variety of general type. Suppose $X$ is of maximal Albanese dimension. We prove that $K^n_X \ge 2 n! \chi(K_X)$