2026/07/07 by Alessio Cela, Sae Koyama
#math.AG
We show that the genuinely enumerative count of algebraic elliptic curves in any toric variety agrees with the count of the corresponding well-spaced tropical curves, weighted by explicit combinatorial multiplicities. This provides a complete genus-1 generalization of the celebrated Nishinou--Siebert correspondence theorem in genus 0. The proof is algebro-geometric and relies on logarithmic deformation theory together with an explicit enumeration of logarithmic maps with fixed tropicalization.