Standard canonical support loci

TL;DR

This paper studies the structure of canonical support loci in complex geometry, proving a theorem that generalizes previous results and applying it to classify certain compact Kähler manifolds with specific invariants.

Contribution

It introduces the concept of standard support loci, proves a structure theorem, and extends classification results to Kähler manifolds.

Findings

Structure theorem for standard support loci

Recovery and improvement of Beauville and Chen-Jiang results

Extension of classification to compact Kähler manifolds with specific invariants

Abstract

We consider the union of certain irreducible components of cohomological support loci of the canonical bundle, which we call standard. We prove a structure theorem about them and single out some particular cases, recovering and improving results of Beauville and Chen-Jiang. Finally, as an example of application, we extend to compact Kahler manifolds the classification of smooth complex projective varieties with $p_1(X)=1$, $p_3(X)=2$ and $q(X)=\dim X$.