21 citations · 66 across the 17 of their papers we have counts for
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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…