3 papers
math.AG2026
Elliptic curve counting in toric threefolds: virtual, enumerative, and tropical
Sae Koyama
We study the enumerative geometry of elliptic curves in toric threefolds. We consider enumerative integer invariants, called well-spaced counts, which can be studied using well-spa…
math.AG2026
Tropical and algebraic elliptic plane curves with fixed j-invariant
Alessio Cela, Sae Koyama
We tropically enumerate planar well-spaced elliptic curves with a fixed -invariant. Combined with the recent genus 1 correspondence theorem of Cela--Koyama, this yields an alter…
math.AG2026
Genus one correspondence between tropical and algebraic curves
Alessio Cela, Sae Koyama
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 e…