Some properties and applications of Brieskorn lattices

TL;DR

This paper reviews key properties of Brieskorn lattices for tame regular functions on smooth affine complex varieties and proves a conjecture in the toric case, advancing understanding in algebraic geometry.

Contribution

It establishes the conjecture of Katzarkov-Kontsevich-Pantev for the toric case, providing new insights into Brieskorn lattices.

Findings

Proved the Katzarkov-Kontsevich-Pantev conjecture in the toric case

Reviewed fundamental properties of Brieskorn lattices in the context of tame regular functions

Enhanced understanding of the structure of Brieskorn lattices in algebraic geometry

Abstract

After reviewing the main properties of the Brieskorn lattice in the framework of tame regular functions on smooth affine complex varieties, we prove a conjecture of Katzarkov-Kontsevich-Pantev in the toric case.