6 papers
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…
Enumerating pencils with moving ramification on curves
Carl Lian
We consider the general problem of enumerating branched covers of the projective line from a fixed general curve subject to ramification conditions at possibly moving points. Our m…
The class of the d-elliptic locus in genus 2
Carl Lian
We compute the rational Chow class of the locus of genus 2 curves admitting a d-to-1 map to a genus 1 curve, recovering a result of Faber-Pagani when d=2. The answer exhibits quasi…