Zobrazeno 1 - 10
of 96
pro vyhledávání: '"Przyjalkowski, Victor"'
Publikováno v:
Commun. Number Theory Phys., 18:3 (2024), 509--577
We study the coregularity of smooth Fano threefolds. We prove that for 100 out of 105 families of smooth Fano threefolds, a general member in the family has coregularity 0; moreover, for 92 families out of these 100, any member in the family has core
Externí odkaz:
http://arxiv.org/abs/2309.16784
Autor:
Doran, Charles, Harder, Andrew, Katzarkov, Ludmil, Ovcharenko, Mikhail, Przyjalkowski, Victor
For each Fano threefold, we construct a family of Landau-Ginzburg models which satisfy many expectations coming from different aspects of mirror symmetry; they are log Calabi-Yau varieties with proper potential maps; they admit open algebraic torus c
Externí odkaz:
http://arxiv.org/abs/2307.15607
Autor:
Przyjalkowski, Victor
Publikováno v:
Sib. Math. J. 64:4 (2023), 890--896
In the literature there are two definitions of well formed varieties in weighted projective spaces. According to the first one, well formed variety is the one whose intersection with the singular locus of the ambient weighted projective space has cod
Externí odkaz:
http://arxiv.org/abs/2302.03293
Publikováno v:
Proyecciones (Antofagasta, On line), vol. 41, no. 2, pp. 481-515, Mar. 2022
We survey the approach to mirror symmetry via Laurent polynomials, outlining some of the main conjectures, problems, and questions related to the subject. We discuss: how to construct Landau--Ginzburg models for Fano varieties; how to apply them to c
Externí odkaz:
http://arxiv.org/abs/2112.15339
Autor:
Przyjalkowski, Victor
Publikováno v:
Sb. Math., 213:12 (2022), 1679--1694
We show that smooth varieties of general type which are well formed weighted complete intersections of Cartier divisors have maximal Hodge level, that is, their the rightmost middle Hodge numbers do not vanish. We show that this does not hold in the
Externí odkaz:
http://arxiv.org/abs/2103.07106
Autor:
Przyjalkowski, Victor
Publikováno v:
Sb. Math. 213:1 (2022), 88--108
We consider the procedure that constructs log Calabi-Yau compactifications of weak Landau-Ginzburg models of Fano varieties. We apply it for del Pezzo surfaces and coverings of projective spaces of index one. For the coverings of degree greater then
Externí odkaz:
http://arxiv.org/abs/2102.01388
Publikováno v:
Math. Notes, 109:4 (2021), 609--613
We prove that a smooth well formed Picard rank one Fano complete intersection of dimension at least 2 in a toric variety is a weighted complete intersection.
Comment: Formerly a part of arXiv:2006.01213; 5 pages
Comment: Formerly a part of arXiv:2006.01213; 5 pages
Externí odkaz:
http://arxiv.org/abs/2010.14447
Publikováno v:
Sb. Math. 212:3 (2021), 374--388
We show that every reductive subgroup of the automorphism group of a quasi-smooth well formed weighted complete intersection is a restriction of a subgroup in the automorphism group in the ambient weighted projective space. Also, we provide examples
Externí odkaz:
http://arxiv.org/abs/2006.01213
Autor:
Cheltsov, Ivan, Przyjalkowski, Victor
Publikováno v:
Commun. Number Theory Phys., 16:4 (2022), 673--693
We conjecture that the number of components of the fiber over infinity of Landau--Ginzburg model for a smooth Fano variety $X$ equals the dimension of the anticanonical system of $X$. We verify this conjecture for log Calabi--Yau compactifications of
Externí odkaz:
http://arxiv.org/abs/2005.01534
Publikováno v:
Sibirsk. Mat. Zh., 61:2 (2020), 377--384
We classify smooth Fano weighted complete intersections of large codimension.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/1906.11547