4 papers
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…
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…