Duality for projective morphisms finite in codimension one and the positivity of double point divisors of general inner projections

Abstract

The purpose of this paper is to prove the positivity of double point divisors of general inner projections for projective S₂-varieties with invertible dualizing sheaves, without assuming the smoothness or the normality of varieties. As applications, we characterize two types of projective varieties: varieties with trivial double point divisors and varieties with $d-e-1\le n$ for dimension n, degree d and codimension e.

KEYWORDS:

• Double point divisor
• dualizing sheaf
• linear projection

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 14N05
• 14N15
• 14C20

Additional information

Funding

This paper was partially supported by Grant-in-Aid for Scientific Research (C), 20K03531, 17K05197, and 26400041 Japan Society for the Promotion of Science.