Standard canonical support loci

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 $q(X)=\dim X$.

Dedicated to Philippe Ellia on his 60th birthday. To appear on Rend. Circ. Mat. Palermo

References in corpus (2)

• Regularity on abelian varieties III: relationship with Generic Vanishing and applications
• Hodge modules on complex tori and generic vanishing for compact Kähler manifolds