4 papers
Scrollar invariants of singular curves on toric surfaces
Karl Christ, Xiang He, Ilya Tyomkin
Given a curve on a toric surface, a monomial projection induces a map from the normalization of the curve to the projective line. We determine the associated scrollar invariants fo…
The irreducibility of Hurwitz spaces and Severi varieties on toric surfaces
Karl Christ, Xiang He, Ilya Tyomkin
In 1969, Fulton introduced classical Hurwitz spaces parametrizing simple d-sheeted coverings of the projective line in the algebro-geometric setting. He established the irreducibil…
Balancing properties of tropical moduli maps
Karl Christ, Xiang He, Ilya Tyomkin
Given a family of parameterized algebraic curves over a strictly semistable pair, we show that the simultaneous tropicalization of the curves in the family forms a family of parame…
A note on elliptic curves on toric surfaces
Michael M. Barash, Ilya Tyomkin
In this paper, we study the Severi varieties parametrizing integral curves of geometric genus one on polarized toric surfaces in characteristic zero and describe their irreducible…