Details
| Original language | English |
|---|---|
| Pages (from-to) | 197-240 |
| Number of pages | 44 |
| Journal | Journal für die reine und angewandte Mathematik |
| Volume | 2022 |
| Issue number | 787 |
| Early online date | 1 Apr 2022 |
| Publication status | Published - 1 Jun 2022 |
Abstract
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- General Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal für die reine und angewandte Mathematik, Vol. 2022, No. 787, 01.06.2022, p. 197-240.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Degeneration of curves on some polarized toric surfaces
AU - Christ, Karl
AU - He, Xiang
AU - Tyomkin, Ilya
N1 - Publisher Copyright: © 2022 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2022/6/1
Y1 - 2022/6/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85126089961&partnerID=8YFLogxK
U2 - 10.1515/crelle-2022-0006
DO - 10.1515/crelle-2022-0006
M3 - Article
VL - 2022
SP - 197
EP - 240
JO - Journal für die reine und angewandte Mathematik
JF - Journal für die reine und angewandte Mathematik
SN - 0075-4102
IS - 787
ER -