Zobrazeno 1 - 10
of 116
pro vyhledávání: '"Itenberg, Ilia"'
Autor:
Degtyarev, Alex, Itenberg, Ilia
We prove that the equisingular deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, \ie, the polarization, exceptional divisors, and real structure recorded in the homology of the cove
Externí odkaz:
http://arxiv.org/abs/2403.01252
Autor:
Itenberg, Ilia, Shustin, Eugenii
We introduce new invariants of the projective plane (and, more generally, of certain toric surfaces) that arise from the appropriate enumeration of real curves of genera one and two. These invariants admit a refinement (according to the quantum index
Externí odkaz:
http://arxiv.org/abs/2401.06718
Autor:
Itenberg, Ilia, Shustin, Eugenii
We introduce new invariants of the projective plane (and, more generally, of certain toric surfaces) that arise from the appropriate enumeration of real elliptic curves. These invariants admit a refinement (according to the quantum index) similar to
Externí odkaz:
http://arxiv.org/abs/2303.06203
Publikováno v:
Algebr. Geom. 10 (2023), no. 2, 228--258
We show that the maximal number of planes in a complex smooth cubic fourfold in ${\mathbb P}^5$ is $405$, realized by the Fermat cubic only; the maximal number of real planes in a real smooth cubic fourfold is $357$, realized by the so-called Clebsch
Externí odkaz:
http://arxiv.org/abs/2105.13951
Autor:
Itenberg, Ilia, Mikhalkin, Grigory
For a real K3-surface $X$, one can introduce areas of connected components of the real point set $\mathbb{R} X$ of $X$ using a holomorphic symplectic form of $X$. These areas are defined up to simultaneous multiplication by a positive real number, so
Externí odkaz:
http://arxiv.org/abs/2001.06871
Publikováno v:
European Journal of Mathematics, 5 (2019), no. 3, 686--711
We address the problem of the maximal finite number of real points of a real algebraic curve (of a given degree and, sometimes, genus) in the projective plane. We improve the known upper and lower bounds and construct close to optimal curves of small
Externí odkaz:
http://arxiv.org/abs/1807.03992
The surfaces considered are real, rational and have a unique smooth real $(-2)$-curve. Their canonical class $K$ is strictly negative on any other irreducible curve in the surface and $K^2>0$. For surfaces satisfying these assumptions, we suggest a c
Externí odkaz:
http://arxiv.org/abs/1611.02938
Autor:
Itenberg, Ilia, Zvonkine, Dimitri
Publikováno v:
Commentarii Mathematici Helvetici, 93 (2018), Issue 3, pp. 441--474
We consider the problem of defining and computing real analogs of polynomial Hurwitz numbers, in other words, the problem of counting properly normalized real polynomials with fixed ramification profiles over real branch points. We show that, provide
Externí odkaz:
http://arxiv.org/abs/1609.05219
Publikováno v:
Mathematische Annalen, 374 (1-2), pp. 963-1006 (2019)
Given a tropical variety X and two non-negative integers p and q we define homology group $H_{p,q}(X)$. We show that if X is a smooth tropical variety that can be represented as the tropical limit of a 1-parameter family of complex projective varieti
Externí odkaz:
http://arxiv.org/abs/1604.01838
Publikováno v:
Math. Ann., 368 (2017), 753--809
We show that the maximal number of (real) lines in a (real) nonsingular spatial quartic surface is 64 (respectively, 56). We also give a complete projective classification of all quartics containing more than 52 lines: all such quartics are projectiv
Externí odkaz:
http://arxiv.org/abs/1601.04238