Limits of dual curves via foliations

TL;DR

This paper introduces a method to compute the limits of dual plane curves within Zeuthen families, focusing on the ramification schemes of general linear systems on generic fibers.

Contribution

It provides a novel approach to calculating limits of dual curves and ramification schemes in Zeuthen families, applicable to various types of these families.

Findings

Method to compute limits of dual plane curves

Calculation of limit 0-cycle of ramification schemes

Applicable to Zeuthen families of any kind

Abstract

We develop a method to compute limits of dual plane curves in Zeuthen families of any kind. More precisely, we compute the limit 0-cycle of the ramification scheme of a general linear system on the generic fiber, only assumed geometrically reduced, of a Zeuthen family of any kind.