Department of Mathematics
Two kinds of real lines on real del Pezzo surfaces of degree 1
Finashin, Sergey (2021-11-01)
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 surfa...
Segre Indices and Welschinger Weights as Options for Invariant Count of Real Lines
Finashin, Sergey (2021-03-01)
In our previous paper [5] we have elaborated a certain signed count of real lines on real hypersurfaces of degree 2n - 1 in Pn+1. Contrary to the honest "cardinal" count, it is independent of the choice of a hypersurface a...
The first homology of a real cubic is generated by lines
Finashin, Sergey (2021-01-01)
Chirality of real non-singular cubic fourfolds and their pure deformation classification
Finashin, Sergey (Springer Science and Business Media LLC, 2020-02-22)
In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coeffic...
Finashin, Sergey (American Mathematical Society (AMS), 2019-09-01)
A famous configuration of 27 lines on a non-singular cubic surface in P-3 contains remarkable subconfigurations, and in particular the ones formed by six pairwise disjoint lines. We study such six-line configurations in th...
Deformation Classification of Real Non-singular Cubic Threefolds with a Marked Line
Finashin, Sergey (2018-12-19)
© 2019, Institute for Mathematical Sciences (IMS), Stony Brook University, NY. We prove that the space of pairs (X, l) formed by a real non-singular cubic hypersurface X⊂ P 4 with a real line l⊂ X has 18 connected componen...
Deformation classification of typical configurations of 7 points in the real projective plane
Finashin, Sergey (2015-10-01)
A configuration of 7 points in RP2 is called typical if it has no collinear triples and no coconic sextuples of points. We show that there exist 14 deformation classes of such configurations. This yields classification of ...
Abundance of 3-Planes on Real Projective Hypersurfaces
Finashin, Sergey (2015-07-01)
© 2015, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.We show that a generic real projective n-dimensional hypersurface of odd degree d, such that 4(n-2)=(d+33), contains “many” real 3-planes, namel...
Abundance of Real Lines on Real Projective Hypersurfaces
Finashin, Sergey (2013-01-01)
We show that a generic real projective n-dimensional hypersurface of degree 2n-1 contains many real lines, namely not less than (2n-1)!!, which is approximately the square root of the number of complex lines. This estimate...
Topology of real cubic fourfolds
Finashin, Sergey (2010-01-01)
A solution of the problem of topological classification of real cubic fourfolds is given. It is proven that the real locus of a real non-singular cubic fourfold is diffeomorphic either to a connected sum RP(4)#i(S(2) x S(2...
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