The pluricanonical systems of a product-quotient variety

TL;DR

This paper introduces a method to compute the plurigenera of product-quotient manifolds, aiding in constructing Calabi-Yau threefolds and determining minimal models of certain surfaces.

Contribution

It provides a novel computational approach for plurigenera of product-quotient varieties with applications in Calabi-Yau and minimal model theory.

Findings

Method for computing plurigenera of product-quotient manifolds

Applications to constructing Calabi-Yau threefolds

Determination of minimal models for product-quotient surfaces

Abstract

We give a method for the computation of the plurigenera of a product-quotient manifold. We give two different types of applications to it: to the construction of Calabi-Yau threefolds and to the determination of the minimal model of a product-quotient surface of general type.