A Lemma of Lazarsfeld and the Jacobian blow up

TL;DR

This paper explores the structure of the exceptional divisor in the Jacobian blow-up of a complex analytic function, leveraging a lemma from Lazarsfeld's thesis to deepen understanding of its geometric properties.

Contribution

It reveals new insights into the structure of the exceptional divisor in Jacobian blow-ups using Lazarsfeld's lemma, connecting complex analysis and algebraic geometry.

Findings

Characterization of the exceptional divisor's structure

Application of Lazarsfeld's lemma to Jacobian blow-up

Enhanced understanding of complex analytic function singularities

Abstract

For a complex analytic function $f$, the exceptional divisor of the jacobian blow-up is of great importance. In this paper, we show what a lemma from the thesis of Lazarsfeld tells one about the structure of this exceptional divisor.