Generalized De Jonquieres divisors on generic curves

TL;DR

This paper investigates the enumerative validity of classical De Jonquieres and MacDonald formulas for counting divisors with prescribed multiplicities on general algebraic curves, establishing an essentially optimal result.

Contribution

It proves the enumerative accuracy of these classical formulas for general curves of genus g, extending their applicability.

Findings

Classical formulas are valid for general curves of genus g

Established an essentially optimal enumerative result

Enhanced understanding of divisor counting on algebraic curves

Abstract

The classical De Jonquieres and MacDonald formulas describe the virtual number of divisors with prescribed multiplicities in a linear system on an algebraic curve. We establish an essentially optimal result concerning the enumerative validity of these formulas in the case of a general curve of genus g.