4 papers
math.AG2026
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…
math.AG2026
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…
math.AG2025
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…
math.AG2025
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…