Degeneration of curves on some polarized toric surfaces

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Karl Christ
  • Xiang He
  • Ilya Tyomkin

Organisationseinheiten

Externe Organisationen

  • Ben-Gurion University of the Negev (BGU)
  • Hebrew University of Jerusalem (HUJI)
  • Tsinghua University
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Details

OriginalspracheEnglisch
Seiten (von - bis)197-240
Seitenumfang44
FachzeitschriftJournal für die reine und angewandte Mathematik
Jahrgang2022
Ausgabenummer787
Frühes Online-Datum1 Apr. 2022
PublikationsstatusVeröffentlicht - 1 Juni 2022

Abstract

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 irreducibility of Severi varieties of a large class of polarized toric surfaces with h-transverse polygon.

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Degeneration of curves on some polarized toric surfaces. / Christ, Karl; He, Xiang; Tyomkin, Ilya .
in: Journal für die reine und angewandte Mathematik, Jahrgang 2022, Nr. 787, 01.06.2022, S. 197-240.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Christ K, He X, Tyomkin I. Degeneration of curves on some polarized toric surfaces. Journal für die reine und angewandte Mathematik. 2022 Jun 1;2022(787):197-240. Epub 2022 Apr 1. doi: 10.1515/crelle-2022-0006
Christ, Karl ; He, Xiang ; Tyomkin, Ilya . / Degeneration of curves on some polarized toric surfaces. in: Journal für die reine und angewandte Mathematik. 2022 ; Jahrgang 2022, Nr. 787. S. 197-240.
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