2 citations · 4 across the 13 of their papers we have counts for
13 papers
Brill-Noether existence with secants
Alessio Cela, Carl Lian
We completely characterize when a general curve of genus admits a non-degenerate degree map to projective space , that is -secant along a linear space $\ma…
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…
Pseudo-holomorphic curves with a fixed complex structure in positive symplectic manifolds
Alessio Cela, Aleksander Doan
We prove a symplectic version of a conjecture of Lian and Pandharipande: in sufficiently high degree, the fixed-domain Gromov-Witten invariants of positive symplectic manifolds are…
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…
Genus 0 logarithmic and tropical fixed-domain counts for Hirzebruch surfaces
Alessio Cela, Aitor Iribar Lopez
For a non-singular projective toric variety , the virtual logarithmic Tevelev degrees are defined as the virtual degree of the morphism from the moduli stack of logarithmic stab…
Fixed-domain curve counts for blow-ups of projective space
Alessio Cela, Carl Lian
We study the problem of counting pointed curves of fixed complex structure in blow-ups of projective space at general points. The geometric and virtual (Gromov-Witten) counts are f…
Quantum Euler class and virtual Tevelev degrees of Fano complete intersections
Alessio Cela
We compute the quantum Euler class of Fano complete intersections X in a projective space. In particular, we prove a recent conjecture of A. Buch and R. Pandharipande. Finally we a…
Generalized Tevelev degrees of
Alessio Cela, Carl Lian
Let be a general curve. We consider the problem of enumerating covers of the projective line by subject to incidence conditions at the marked points. These…
Tevelev degrees and Hurwitz moduli spaces
Alessio Cela, Rahul Pandharipande, Johannes Schmitt
We interpret the degrees which arise in Tevelev's study of scattering amplitudes in terms of moduli spaces of Hurwitz covers. Via excess intersection theory, the boundary geometry…