Nonemptiness of severi varieties on enriques surfaces

被引：1

作者：

Ciliberto, Ciro ^{[1
]}

Dedieu, Thomas ^{[2
]}

Galati, Concettina ^{[3
]}

Knutsen, Andreas Leopold ^{[4
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Scientif, I-00173 Rome, Italy

[2] Univ Toulouse, Inst Math Toulouse, CNRS, UMR5219, F-31062 Toulouse 9, France

[3] Univ Calabria, Dipartimento Matemat Informat, Via P Bucci,Cubo 31B, I-87036 Arcavacata Di Rende, CS, Italy

[4] Univ Bergen, Dept Math, Postboks 7800, N-5020 Bergen, Norway

来源：

FORUM OF MATHEMATICS SIGMA | 2023年 / 11卷

基金：

欧盟地平线“2020”;

关键词：

14H20; 14J28; 14D06; 14H10; 14J10; RATIONAL CURVES; NODAL CURVES; ABELIAN SURFACES; FAMILIES; SPACES; PROOF;

D O I：

10.1017/fms.2023.47

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (S, L) be a general polarised Enriques surface, with L not numerically 2-divisible. We prove the existence of regular components of all Severi varieties of irreducible nodal curves in the linear system |L |, that is, for any number of nodes d = 0, ... , p(a) (L) -1. This solves a classical open problem and gives a positive answer to a recent conjecture of Pandharipande-Schmitt, under the additional condition of non-2-divisibility.

引用

页数：32

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