2 citations · 3 across the 5 of their papers we have counts for
8 papers · 1 filter
Degenerations of complete collineations and geometric Tevelev degrees of
Carl Lian
We consider the problem of enumerating maps of degree from a fixed general curve of genus to satisfying incidence conditions of the form $f(p_i)\in X…
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…
Z/rZ-equivariant covers of P^1 with moving ramification
Carl Lian, Riccardo Moschetti
Let X -> P^1 be a general cyclic cover. We give a simple formula for the number of equivariant meromorphic functions on X subject to ramification conditions at variable points. Thi…
Non-tautological Hurwitz cycles
Carl Lian
We show that various loci of stable curves of sufficiently large genus admitting degree covers of positive genus curves define non-tautological algebraic cycles on $\overline{\…
An asymptotic Alexander-Hirschowitz theorem for surfaces
Carl Lian
Let X be a smooth projective surface over C and let L be an ample line bundle on X. In this note, we show that, for all sufficiently large d, any number of general double points on…
The H-tautological ring
Carl Lian
We extend the theory of tautological classes on moduli spaces of stable curves to the more general setting of moduli spaces of admissible Galois covers of curves, introducing the s…