The genuinely enumerative count of elliptic curves in a toric variety equals the tropical count of well-spaced genus-one curves with explicit lattice-polytope multiplicities.
Remarks on gluing punctured logarithmic maps
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We consider some well-behaved cases of the gluing formalism for punctured stable log maps of Abramovich-Chen-Gross-Siebert. This gives a gluing formula for log Gromov-Witten invariants in a diverse set of cases; in particular, the gluing formulae of Li-Ruan, Jun Li and Kim-Lho-Ruddat become an easy special case. The last section gives an application of this gluing formalism to canonical wall structures for K3 surfaces as constructed by Gross and Siebert in "The canonical wall structure and intrinsic mirror symmetry."
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Genus one correspondence between tropical and algebraic curves
The genuinely enumerative count of elliptic curves in a toric variety equals the tropical count of well-spaced genus-one curves with explicit lattice-polytope multiplicities.