Invariance of plurigenera and Chow-type lemma

TL;DR

This paper proves the invariance of plurigenera in certain families of algebraic varieties and introduces Chow-type lemmata to analyze the structure of these families, advancing understanding in algebraic geometry.

Contribution

It establishes the deformation invariance of plurigenera for families with canonical singularities and provides new Chow-type lemmata for projective complex analytic spaces.

Findings

Proves invariance of plurigenera for families with canonical singularities.

Introduces Chow-type lemmata for the structure of projective complex analytic families.

Extends results to families with uncountable members of general type.

Abstract

This paper answers a question of Demailly whether a smooth family of nonsingular projective varieties admits the deformation invariance of plurigenera affirmatively, and proves this more generally for a flat family of varieties with only canonical singularities and uncountable ones therein being of general type and also two Chow-type lemmata on the structure of a family of projective complex analytic spaces.