4 papers · 1 filter
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…
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…
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…
Constructions of superabundant tropical curves in higher genus
Sae Koyama
We construct qualitatively new examples of superabundant tropical curves which are non-realizable in genus and . These curves are in and respec…