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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…