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

2021/02/09 by Sergey Finashin, Finashin, Sergey, Viatcheslav Kharlamov +1 · 1 citation
Mathematics · #14J26 #14N10 (Primary) #14N15 (Secondary) #14P25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.GT #msc:14J26 #msc:14N10 #msc:14N15 #msc:14P25

paper · pdf · doi:10.48550/arxiv.2102.04713

19 pages, 5 figures

arxiv created 2021/02/09 · arxiv updated 2021/02/10

Abstract

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.

Cited by

• A quadratically enriched count of lines on a smooth del Pezzo surface of degree 5

Related

• The real Mordell-Weil group of rational elliptic surfaces and real lines on del Pezzo surfaces of degree K²=1
• Full Degree Two del Pezzo Surfaces over Small Finite Fields
• Intrinsic signs and lower bounds in real algebraic geometry
• Concurrent lines on del Pezzo surfaces of degree one
• Floor diagrams relative to a conic, and GW-W invariants of Del Pezzo surfaces