Zobrazeno 1 - 10
of 112
pro vyhledávání: '"Kharlamov, Viatcheslav"'
We undertake a study of topological properties of the real Mordell-Weil group $\operatorname{MW}_{\mathbb R}$ of real rational elliptic surfaces $X$ which we accompany by a related study of real lines on $X$ and on the "subordinate" del Pezzo surface
Externí odkaz:
http://arxiv.org/abs/2409.01202
We give an expression for the Smith-Thom deficiency of the Hilbert square $X^{[2]}$ of a smooth real algebraic variety $X$ in terms of the rank of a suitable Mayer-Vietoris mapping in several situations. As a consequence, we establish a necessary and
Externí odkaz:
http://arxiv.org/abs/2310.19120
We explore the maximality of the Hilbert square of maximal real surfaces, and find that in many cases the Hilbert square is maximal if and only if the surface has connected real locus. In particular, the Hilbert square of no maximal K3-surface is max
Externí odkaz:
http://arxiv.org/abs/2303.02796
We prove that the space of affine, transversal at infinity, non-singular real cubic surfaces has 15 connected components. We give a topological criterion to distinguish them and show also how these 15 components are adjacent to each other via wall-cr
Externí odkaz:
http://arxiv.org/abs/2208.09502
We continue our quest for real enumerative invariants not sensitive to changing the real structure and extend the construction we uncovered previously for counting curves of anti-canonical degree $\leqslant 2$ on del Pezzo surfaces with $K^2=1$ to cu
Externí odkaz:
http://arxiv.org/abs/2203.10503
Combined count of real rational curves of canonical degree 2 on real del Pezzo surfaces with $K^2=1$
We propose two systems of "intrinsic" signs for counting such curves. In both cases the result acquires an exceptionally strong invariance property: it does not depend on the choice of a surface. One of our counts includes all divisor classes of cano
Externí odkaz:
http://arxiv.org/abs/2107.06988
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 splittin
Externí odkaz:
http://arxiv.org/abs/2102.04713
This paper was conceived as an addendum to the note "Rokhlin's signature theorems" (by O.Viro and the authors of this paper). In the main section we give an overview of Rokhlin's proof of his famous theorem on divisibility of signature by 16. In the
Externí odkaz:
http://arxiv.org/abs/2012.06389
This note is written for a book dedicated to outstanding St-Petersburg mathematicians and timed to the ICM-2022 in St-Petersburg. In accordance with the plan of ICM-organizers, we try to tell about one of the most prominent Rokhlin's achievements in
Externí odkaz:
http://arxiv.org/abs/2012.02004
This is an expanded version of the talk given be the first author at the conference "Topology, Geometry, and Dynamics: Rokhlin - 100". The purpose of this talk was to explain our current results on classification of rational symplectic 4-manifolds eq
Externí odkaz:
http://arxiv.org/abs/2005.03142