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pro vyhledávání: '"Degtyarev, Alex"'
Autor:
Degtyarev, Alex
We prove that the maximal number of conics, a priori irreducible of reducible, on a smooth spatial quartic surface is 800, realized by a unique quartic. We also classify quartics with many (at least 720) conics. The maximal number of real conics on a
Externí odkaz:
http://arxiv.org/abs/2407.00493
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:
Degtyarev, Alex, Rams, Sławomir
We prove the sharp upper bound of at most $52$ lines on a complex K3-surface of degree four with a non-empty singular locus. We also classify the configurations of more than $48$ lines on smooth complex quartics.
Comment: 22 pages, extra data av
Comment: 22 pages, extra data av
Externí odkaz:
http://arxiv.org/abs/2301.04127
Autor:
Degtyarev, Alex
Publikováno v:
Science China Mathematics, Vol. 67 (July 2024) No. 7: 1507--1524
We analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by $176$ and show that there is a unique surface with $176$ conics, all irreducible: it admits a faithful acti
Externí odkaz:
http://arxiv.org/abs/2210.06966
Publikováno v:
Algebr. Geom. Topol. 24 (2024) 1101-1120
The slope is an isotopy invariant of colored links with a distinguished component, initially introduced by the authors to describe an extra correction term in the computation of the signature of the splice. It appeared to be closely related to severa
Externí odkaz:
http://arxiv.org/abs/2202.04529
Autor:
Degtyarev, Alex
Publikováno v:
Tohoku Math. J. (2)75(2023), no.3, 395--421
We classify the configurations of lines and conics in smooth Kummer quartics, assuming that all $16$ Kummer divisors map to conics. We show that the number of conics on such a quartic is at most $800$.
Externí odkaz:
http://arxiv.org/abs/2108.11181
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:
Degtyarev, Alex, Rams, Sławomir
We combine classical Vinberg's algorithms with the lattice-theoretic/arithmetic approach from arXiv:1706.05734 [math.AG] to give a method of classifying large line configurations on complex quasi-polarized K3-surfaces. We apply our method to classify
Externí odkaz:
http://arxiv.org/abs/2104.04583
Autor:
Degtyarev, Alex
Publikováno v:
J. Pure Appl. Algebra 226 (2022), no. 10, Paper No. 107077, 5 pp
We construct an example of a smooth spatial quartic surface that contains 800 irreducible conics.
Comment: The paper reflects the considerable development (explicit equations by X. Roulleau and B. Naskrecki) that followed the original version
Comment: The paper reflects the considerable development (explicit equations by X. Roulleau and B. Naskrecki) that followed the original version
Externí odkaz:
http://arxiv.org/abs/2102.08163
Autor:
Degtyarev, Alex
Publikováno v:
Nagoya Math. J. 246 (2022), 273--304
We prove that the maximal number of conics in a smooth sextic $K3$-surface $X\subset\mathbb{P}^4$ is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible.
Comment: Fi
Comment: Fi
Externí odkaz:
http://arxiv.org/abs/2010.07412