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

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 rea...

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Bibliographic Details
Published in:Selecta mathematica (Basel, Switzerland) Switzerland), 2021-11, Vol.27 (5), Article 83
Main Authors: Finashin, S., Kharlamov, V.
Format: Article
Language:English
Subjects:
Algebraic Geometry
Algebraic Topology
Automorphisms
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-021-00690-x