Cone and contraction theorem for projective morphisms between complex analytic spaces

TL;DR

This paper extends the cone and contraction theorem to projective morphisms between complex analytic spaces, providing foundational results for the minimal model program in complex analytic geometry, especially for pairs with severe singularities.

Contribution

It establishes the cone and contraction theorem for normal pairs with complex analytic projective morphisms, advancing the minimal model program for complex analytic spaces.

Findings

Proves the cone and contraction theorem in a complex analytic setting.

Provides a foundation for the minimal model program in complex analytic geometry.

Addresses cases with worse-than-kawamata log terminal singularities.

Abstract

We discuss the cone and contraction theorem in a suitable complex analytic setting. More precisely, we establish the cone and contraction theorem of normal pairs for projective morphisms between complex analytic spaces. This result is a starting point of the minimal model program for complex analytic log canonical pairs. In this paper, we are mainly interested in normal pairs whose singularities are worse than kawamata log terminal singularities.