# Secant planes of a general curve via degenerations

## TL;DR

This paper investigates special secant planes of general algebraic curves by studying linear series and their degenerations, providing formulas for counting exceptional secant configurations.

## Contribution

It introduces a moduli scheme for limit linear series with base points and derives combinatorial formulas for counting secant-exceptional linear series.

## Key findings

- Constructed a moduli scheme for inclusions of limit linear series with base points.
- Derived formulas for the number of secant-exceptional linear series in finite cases.
- Connected secant plane geometry with degenerations and enumerative geometry.

## Abstract

We study linear series on a general curve of genus g, whose images are exceptional with respect to their secant planes. Each such exceptional secant plane is algebraically encoded by an included linear series, whose number of base points computes the incidence degree of the corresponding secant plane. With enumerative applications in mind, we construct a moduli scheme of inclusions of limit linear series with base points over families of nodal curves of compact type, which we then use to compute combinatorial formulas for the number of secant-exceptional linear series when the spaces of linear series and of inclusions are finite.