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math.AG2025
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…
math.AG2025
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…