Two kinds of real lines on real del Pezzo surfaces of degree 1

被引：2
|
作者：
Finashin, S. [1 ]
Kharlamov, V [2 ,3 ]
机构：
[1] Middle East Tech Univ, Ankara, Turkey
[2] Univ Strasbourg, Strasbourg, France
[3] IRMA, CNRS, Strasbourg, France
来源：
SELECTA MATHEMATICA-NEW SERIES | 2021年 / 27卷 / 05期
关键词：
Real del Pezzo surfaces; Enumerative invariants; Counting real lines; Pin-structures; Elliptic and hyperbolic lines;
D O I：
10.1007/s00029-021-00690-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show how the real lines on a real del Pezzo surface of degree 1 can be split into two species, elliptic and hyperbolic, via a certain distinguished, intrinsically defined, Pin(-)-structure on the real locus of the surface. We prove that this splitting is invariant under real automorphisms and real deformations of the surface, and that the difference between the total numbers of hyperbolic and elliptic lines is always equal to 16.
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页数：23
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