Department of Mathematics
Segre Indices and Welschinger Weights as Options for Invariant Count of Real Lines
Finashin, Sergey; Kharlamov, Viatcheslav (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...
Chirality of real non-singular cubic fourfolds and their pure deformation classification
Finashin, Sergey; Kharlamov, V (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; Zabun, Remziye Arzu (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 typical configurations of 7 points in the real projective plane
Finashin, Sergey; Zabun, Remziye Arzu (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 Real Lines on Real Projective Hypersurfaces
Finashin, Sergey; Kharlamov, Viatcheslav (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; Kharlamov, V. (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...
On the deformation chirality of real cubic fourfolds
Finashin, Sergey; Kharlamov, V. (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 de...
Finashin, Sergey; Kharlamov, V. (2008-10-01)
We study real nonsingular cubic hypersurfaces X subset of P-5 up to deformation equivalence combined with projective equivalence and prove that, they, are classified by the conjugacy classes of involutions induced by the c...
Knotting of algebraic curves in CP2
Finashin, Sergey (2002-01-01)
For any k⩾3, I construct infinitely many pairwise smoothly non-isotopic smooth surfaces homeomorphic to a non-singular algebraic curve of degree 2k, realizing the same homology class as such a curve and having abelian fun...
Decomposability of quotients by complex conjugation for rational and Enriques surfaces
Finashin, Sergey (1997-09-02)
The quotients Y = X/conj by the complex conjugation conj:X --> X for complex rational and Enriques surfaces X defined over R are shown to be diffeomorphic to connected sums of <(CP)over bar>(2), whenever the Y are simply c...
Citation Formats