Some applications of Grothendieck Duality Theorem

TL;DR

This paper demonstrates how Grothendieck duality theorem can be systematically used to simplify proofs of various theorems in algebraic geometry, highlighting a unifying approach across multiple results.

Contribution

It introduces a unified method leveraging Grothendieck duality to streamline proofs of several key theorems in algebraic geometry.

Findings

Simplified proofs of vanishing theorems in KMM and Kovács

Unified approach to multiple theorems using Grothendieck duality

Identification of a common trick applicable across different results

Abstract

In this paper, we systematically apply Grothendieck duality theorem to simplify the proofs of several theorems in different papers: Including a vanishing theorem in KMM, a theorem of Koll\'{a}r's paper, a vanishing theorem due to Kov\'{a}cs and a theorem of Fujino. We remark that all of the above are achieved by the same trick.