Tropical Tevelev degrees

TL;DR

This paper introduces tropical Tevelev degrees as tropical analogs of algebraic degrees, providing explicit combinatorial formulas and proving their equivalence with algebraic invariants.

Contribution

It defines tropical Tevelev degrees, develops a combinatorial method to compute them as 2^g, and proves their agreement with algebraic degrees.

Findings

Tropical Tevelev degrees are computed as 2^g.

Tropical and algebraic degrees are shown to agree.

Explicit combinatorial construction for tropical degrees.

Abstract

We define the tropical Tevelev degrees, $\mathsf{Tev}_g^{trop}$, as the degree of a natural finite morphism between certain tropical moduli spaces, in analogy to the algebraic case. We develop an explicit combinatorial construction that computes $\mathsf{Tev}_g^{trop} = 2^g$. We prove that these tropical enumerative invariants agree with their algebraic counterparts, giving an independent tropical computation of the algebraic degrees $Tev_g$.