8 papers · 1 filter
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…
Interpolation for rational curves with secants
Alessio Cela, Carl Lian
In arbitrary characteristic, we determine the maximum number of general points through which a rational curve of degree in passes, subject to an additional secan…
Complete quasimaps to
Alessio Cela, Carl Lian
We introduce a moduli space of ``complete quasimaps'' to . The construction, following previous work for curves on projective spaces, esse…
Curves on Hirzebruch Surfaces and Semistability
Alessio Cela, Carl Lian
When , we show that a general pointed curve never interpolates through the expected number of points in the Hirzebruch surface , with one exception. In the ex…
A Brill-Noether Theorem for (toric) surfaces
Alessio Cela, Carl Lian
The classical Brill-Noether theorem states that a map from a general curve to a projective space deforms in a family of expected dimension as long as its image does not lie in any…