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- Ilia Itenberg, V. M. Kharlamov, Eugenii Shustin
- 2003

Welschinger’s invariant bounds from below the number of real rational curves through a given generic collection of real points in the real projective plane. We estimate this invariant using Mikhalkin’s approach which deals with a corresponding count of tropical curves. In particular, our estimate implies that, for any positive integer d, there exists a real… (More)

- V. M. Kharlamov
- 2007

We introduce and begin the topological study of real rational plane curves, all of whose inflection points are real. The existence of such curves is a corollary of results in the real Schubert calculus, and their study has consequences for the important Shapiro and Shapiro conjecture in the real Schubert calculus. We establish restrictions on the number of… (More)

- Ilia Itenberg, V. M. Kharlamov, Eugenii Shustin
- 2008

The Welschinger numbers, a kind of a real analog of the Gromov-Witten numbers which count the complex rational curves through a given generic collection of points, bound from below the number of real rational curves for any real generic collection of points. By the logarithmic equivalence of sequences we mean the asymptotic equivalence of their logarithms.… (More)

We introduce and develop a language of semigroups over the braid groups for a study of braid monodromy factorizations (bmf's) of plane algebraic curves and other related objects. As an application we give a new proof of Orevkov's theorem on realization of a bmf over a disc by algebraic curves and show that the complexity of such a realization can not be… (More)

- S. Finashin, V. M. Kharlamov
- 2006

We study real nonsingular cubic hypersurfaces X ⊂ 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 complex conjugation in H4(X). Moreover, we provide a graph ΓK4 whose vertices represent the equivalence classes of such cubics and edges represent… (More)

We construct several rigid (i.e., unique in their deformation class) surfaces which have particular behavior with respect to real structures: in one example the surface has no any real structure, in the other one it has a unique real structure and this structure is not maximal with respect to the Smith-Thom inequality. So, it answers in negative to the… (More)

- V. M. Kharlamov
- 2001

In this paper we prove that there is an infinite sequence of pairs of plane cuspidal curves Cm,1 and Cm,2, such that the pairs (CP, Cm,1) and (CP, Cm,2) are diffeomorphic, but Cm,1 and Cm,2 have non-equivalent braid monodromy factorizations. These curves give rise to the negative solutions of ”Dif=Def” and ”Dif=Iso” problems for plane irreducible cuspidal… (More)

- Alex Degtyarev, Ilia Itenberg, V. M. Kharlamov, V. M. Kharlamov
- 2006

We study real elliptic surfaces and trigonal curves (over a base of an arbitrary genus) and their equivariant deformations. We calculate the real TateShafarevich group and reduce the deformation classification to the combinatorics of a real version of Grothendieck’s dessins d’enfants. As a consequence, we obtain an explicit description of the deformation… (More)

- Florian Deloup, Vladimir Turaev, Thomas Fiedler, V. M. Kharlamov, Christine Lescop
- 1997

2 3 a Florence, a mes parents, a Aur elien, 4 5 Remerciements C'est un v eritable plaisir pour moi de remercier Vladimir Turaev a qui je dois tant. Depuis le d ebut du travail, o u Vladimir me proposait une demi-douzaine de sujets de th ese, jusqu'aux derniers d etails, sa gentillesse, sa patience et sa sagesse m'ont guid e. Je suis reconnaissant a Thomas… (More)

- Alex Degtyarev, V. M. Kharlamov, V. M. Kharlamov
- 2002

We compare the smooth and deformation equivalence of actions of finite groups on K3-surfaces by holomorphic and anti-holomorphic transformations. We prove that the number of deformation classes is finite and, in a number of cases, establish the expected coincidence of the two equivalence relations. More precisely, in these cases we show that an action is… (More)