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 real deformations of the surface, and that the difference between the total numbers of hyperbolic and elliptic lines is always equal to 16.


Bayesian classification of image structures
Goswami, D.; Kalkan, Sinan; Krüger, N. (2009-11-09)
In this paper, we describe work on Bayesian classifiers for distinguishing between homogeneous structures, textures, edges and junctions. We build semi-local classifiers from hand-labeled images to distinguish between these four different kinds of structures based on the concept of intrinsic dimensionality. The built classifier is tested on standard and non-standard images. © 2009 Springer Berlin Heidelberg.
Classification of automorphism groups of rational elliptic surfaces
Karayayla, Tolga (2011-01-06)
In this work the classification given indicates the possible automorphism groups of relatively minimal rational elliptic surfaces according to the configuration of singular fibers on the surface. A relatively minimal rational elliptic surface is equivalent to the blow-up of the projective plane at the 9 base points of a pencil of cubics whose generic element is a smooth cubic. This pencil gives a map to the projective line. The generic fiber of this map is a smooth elliptic curve but there are also singular...
On symplectic quotients of K3 surfaces
Cinkir, Z; Onsiper, H (Elsevier BV, 2000-12-18)
In this note, we construct generalized Shioda-Inose structures on K3 surfaces using cyclic covers and almost functoriality of Shioda-Inose structures with respect to normal subgroups of a given group of symplectic automorphisms.
On the deformation chirality of real cubic fourfolds
Finashin, Sergey (Wiley, 2009-09-01)
According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...
Semi-discrete hyperbolic equations admitting five dimensional characteristic x-ring
Zheltukhın, Kostyantyn (2016-01-01)
The necessary and sufficient conditions for a hyperbolic semi-discrete equation to have five dimensional characteristic x-ring are derived. For any given chain, the derived conditions are easily verifiable by straightforward calculations.
Citation Formats
S. Finashin, “Two kinds of real lines on real del Pezzo surfaces of degree 1,” SELECTA MATHEMATICA-NEW SERIES, vol. 27, no. 5, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: