6 citations · 15 across the 16 of their papers we have counts for
18 papers
Curves in projective space and RSK
Carl Lian, Saskia Solotko
The geometric Tevelev degrees of projective space enumerate general, pointed algebraic curves interpolating through the maximal possible number of points. Previous work expresses t…
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…
Torus orbit closures and 1-strip-less tableaux
Carl Lian
We compare two formulas for the class of a generic torus orbit closure on the Grassmannian, due to Klyachko and Berget-Fink. The naturally emerging combinatorial objects are semi-s…
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…
Asymptotic geometric Tevelev degrees of hypersurfaces
Carl Lian
Let be a fixed general pointed curve and let be a smooth hypersurface of degree and dimension with general points. We consider…
Generalized Tevelev degrees of
Alessio Cela, Carl Lian
Let be a general curve. We consider the problem of enumerating covers of the projective line by subject to incidence conditions at the marked points. These…
Enumerativity of virtual Tevelev degrees
Carl Lian, Rahul Pandharipande
Tevelev degrees in Gromov-Witten theory are defined whenever there are virtually a finite number of genus maps of fixed complex structure in a given curve class through …
Linear series on general curves with prescribed incidence conditions
Gavril Farkas, Carl Lian
Using degeneration and Schubert calculus, we consider the problem of computing the number of linear series of given degree and dimension on a general curve of genus sat…
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…
d-elliptic loci in genus 2 and 3
Carl Lian
We consider the loci of curves of genus 2 and 3 admitting a -to-1 map to a genus 1 curve. After compactifying these loci via admissible covers, we obtain formulas for their Chow…
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…
Circular Planar Electrical Networks II: Positivity Phenomena
Joshua Alman, Carl Lian, Brandon Tran
Curtis-Ingerman-Morrow characterize response matrices for circular planar electrical networks as symmetric square matrices with row sums zero and non-negative circular minors. In t…
Circular Planar Electrical Networks I: The Electrical Poset EP_{n}
Joshua Alman, Carl Lian, Brandon Tran
Following de Verdière-Gitler-Vertigan and Curtis-Ingerman-Morrow, we prove a host of new results on circular planar electrical networks. We introduce a poset EP_{n} of electrical n…
Representations of Cherednik Algebras Associated to Symmetric and Dihedral Groups in Positive Characteristic
Carl Lian
We consider irreducible lowest-weight representations of Cherednik algebras associated to certain classes of complex reflection groups in characteristic p. In particular, we study…