21 citations · 66 across the 17 of their papers we have counts for
18 papers
The Geometry of Severi Varieties
Ilya Tyomkin
In this appendix, we summarize known results on the geometry of Severi varieties on toric surfaces - the varieties parameterizing integral curves of a given geometric genus in a gi…
Degeneration of curves on some polarized toric surfaces
Karl Christ, Xiang He, Ilya Tyomkin
We address the following question: Given a polarized toric surface (S,L), and a general integral curve C of geometric genus g in the linear system |L|, do there exist degenerations…
A note on the Severi problem for toric surfaces
Lionel Lang, Ilya Tyomkin
In this note, we make a step towards the classification of toric surfaces admitting reducible Severi varieties. We generalize the results of [Lan19, Tyo13, Tyo14], and provide two…
On the Severi problem in arbitrary characteristic
Karl Christ, Xiang He, Ilya Tyomkin
In this paper, we show that Severi varieties parameterizing irreducible reduced planar curves of a given degree and geometric genus are either empty or irreducible in any character…
Reduction and lifting problem for differential forms on Berkovich curves
Michael Temkin, Ilya Tyomkin
Given a complete real-valued field of residue characteristic zero, we study properties of a differential form on a smooth proper -analytic curve . In particular, we a…
Tropicalized quartics and canonical embeddings for tropical curves of genus 3
Marvin Anas Hahn, Hannah Markwig, Yue Ren +1
Brodsky, Joswig, Morrison and Sturmfels showed that not all abstract tropical curves of genus can be realized as a tropicalization of a quartic in the euclidean plane. In this…