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Degeneration of curves on some polarized toric surfaces.
- Source :
-
Journal für die Reine und Angewandte Mathematik . Jun2022, Vol. 2022 Issue 787, p197-240. 44p. - Publication Year :
- 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 the irreducibility of Severi varieties of a large class of polarized toric surfaces with h-transverse polygon. [ABSTRACT FROM AUTHOR]
- Subjects :
- *TORIC varieties
*LINEAR systems
*POLYGONS
Subjects
Details
- Language :
- English
- ISSN :
- 00754102
- Volume :
- 2022
- Issue :
- 787
- Database :
- Academic Search Index
- Journal :
- Journal für die Reine und Angewandte Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 157253927
- Full Text :
- https://doi.org/10.1515/crelle-2022-0006