Degeneration of curves on some polarized toric surfaces

Karl Christ, Xiang He, Ilya Tyomkin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 of C in |L| to general integral curves of smaller geometric genera? We give an affirmative answer to this question for surfaces associated to h-transverse polygons, provided that the characteristic of the ground field is large enough. We give examples of surfaces in small characteristic, for which the answer to the question is negative. In case the answer is affirmative, we deduce that a general curve C as above is nodal. In characteristic 0, we use the result to show the irreducibility of Severi varieties of a large class of polarized toric surfaces with h-transverse polygon.

Original languageEnglish
Pages (from-to)197-240
Number of pages44
JournalJournal fur die Reine und Angewandte Mathematik
Issue number787
StatePublished - 1 Jun 2022

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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