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Halphen pencils on quartic threefolds
Advances in Mathematics. 2010. Vol. 223. P. 594-618.
Ivan Cheltsov, Karzhemanov I.
For any smooth quartic threefold in P4 we classify pencils on it whose general element is an irreducible surface birational to a surface of Kodaira dimension zero.
Gritsenko V., Никулин В. В., TRANSACTIONS OF THE MOSCOW MATHEMATICAL SOCIETY 2017 Т. 78 № 1 С. 89-100
Using our results about Lorentzian Kac--Moody algebras and arithmetic mirror symmetry, we give six series of examples of lattice-polarized K3 surfaces with automorphic discriminant. ...
Added: October 11, 2017
Yuri Prokhorov, Constantin Shramov, Compositio Mathematica 2014 Vol. 150 No. 12 P. 2054-2072
Assuming a particular case of the Borisov–Alexeev–Borisov conjecture, we prove that finite subgroups of the automorphism group of a finitely generated field over Q have bounded orders. Further, we investigate which algebraic varieties have groups of birational selfmaps satisfying the Jordan property. Unless explicitly stated otherwise, all varieties are assumed to be algebraic, geometrically irreducible ...
Added: January 29, 2015
Verbitsky M., Geometry and Topology 2014 Vol. 18 No. 2 P. 897-909
A Hermitian metric ω on a complex manifold is called SKT or pluriclosed if ddcω=0. Let M be a twistor space of a compact, anti-selfdual Riemannian manifold, admitting a pluriclosed Hermitian metric. We prove that in this case M is Kähler, hence isomorphic to CP3 or a flag space. This result is obtained from rational ...
Added: April 29, 2014
Golota A., / Cornell University. Series arXiv "math". 2022.
Let X be a complex projective variety. Suppose that the group of birational automorphisms of X contains finite subgroups isomorphic to (ℤ/Niℤ)r for r fixed and Ni arbitrarily large. We show that r does not exceed 2dim(X). We also show that the same result holds for groups of bimeromorphic automorphisms of compact Kähler threefolds. ...
Added: October 4, 2022
Guletski ̆i V., Tikhomirov A. S., Proceedings of the Edinburgh Mathematical Society 2016 Vol. 59 No. 02 P. 377-392
Let τ be the involution changing the sign of two coordinates in ℙ4. We prove that τ induces the identity action on the second Chow group of the intersection of a τ-invariant cubic with a τ-invariant quadric hypersurface in ℙ4. Let lτ andΠτ be the one- and two-dimensional components of the fixed locus of the involution τ. We describe the generalized Prymian associated with the ...
Added: December 28, 2015
Galkin S., Iritani H., / Cornell University. Series math "arxiv.org". 2015. No. 1508.00719.
The asymptotic behaviour of solutions to the quantum differential equation of a Fano manifold F defines a characteristic class A_F of F, called the principal asymptotic class. Gamma conjecture of Vasily Golyshev and the present authors claims that the principal asymptotic class A_F equals the Gamma class G_F associated to Euler's Γ-function. We illustrate in ...
Added: August 5, 2015
Shramov K., / Cornell University. Series arXiv "math". 2019.
We prove that a finite group acting by birational automorphisms of a non-trivial Severi-Brauer surface over a field of characteristic zero contains a normal abelian subgroup of index at most 3. Also, we find an explicit bound for orders of such finite groups in the case when the base field contains all roots of 1. ...
Added: November 19, 2019
Galkin S., Shinder E., / Cornell University. Series math "arxiv.org". 2014. No. 1405.5154.
We find a relation between a cubic hypersurface Y and its Fano variety of lines F(Y) in the Grothendieck ring of varieties. We prove that if the class of an affine line is not a zero-divisor in the Grothendieck ring of varieties, then Fano variety of lines on a smooth rational cubic fourfold is birational ...
Added: May 21, 2014
Kuznetsov A., Perry A., Compositio Mathematica 2018 Vol. 154 No. 7 P. 1362-1406
We study the derived categories of coherent sheaves on Gushel–Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety is even or odd. We analyze the basic properties of this category using Hochschild homology, ...
Added: September 13, 2018
Galkin S., Rybakov S., / Cornell University. Series math "arxiv.org". 2019. No. 1910.14379.
For a family of K3 surfaces we implement a variation of a general construction of towers of algebraic curves over finite fields given in a previous paper. As a result we get a good tower over k=𝔽_{p^2}, that is optimal if p=3. ...
Added: November 6, 2019
Aleksei Golota, International Journal of Mathematics 2020 Vol. 31 No. 10 P. 2050077
For a variety 𝑋, a big ℚ-divisor 𝐿 and a closed connected subgroup 𝐺⊂Aut(𝑋,𝐿) we define a 𝐺-invariant version of the 𝛿-threshold. We prove that for a Fano variety (𝑋,−𝐾_𝑋) and a connected subgroup 𝐺⊂Aut(𝑋) this invariant characterizes 𝐺-equivariant uniform 𝐾-stability. We also use this invariant to investigate 𝐺-equivariant 𝐾-stability of some Fano varieties with ...
Added: September 25, 2020
Kuznetsov A., / Cornell University. Series arXiv "math". 2018.
We show that the derived category of a general Enriques surface can be realized as a semiorthogonal component in the derived category of a smooth Fano variety with a diagonal Hodge diamond. ...
Added: December 3, 2018
Kiritchenko V., Tsfasman M., Vladuts S. et al., / Cornell University. Series arXiv "math". 2023.
Quadratic residue patterns modulo a prime are studied since 19th century. We state the last unpublished result of Lydia Goncharova, reformulate it and prior results in terms of algebraic geometry, and prove it. The core of this theorem is an unexpected relation between the number of points on a K3 surface and that on a ...
Added: December 3, 2023
Galkin S., / Cornell University. Series math "arxiv.org". 2018. No. 1809.02738.
We show that G-Fano threefolds are mirror-modular.
1. Mirror maps are inversed reversed Hauptmoduln for moonshine subgroups of SL2(ℝ).
2. Quantum periods, shifted by an integer constant (eigenvalue of quantum operator on primitive cohomology) are expansions of weight 2 modular forms (theta-functions) in terms of inversed Hauptmoduln.
3. Products of inversed Hauptmoduln with some fractional powers of shifted ...
Added: September 25, 2018
Vladimir L. Popov, Springer Proceedings in Mathematics & Statistics 2014 Vol. 79 P. 185-213
This is an expanded version of my talk at the workshop
``Groups of Automorphisms in Birational and Affine Geometry'',
October 29–November 3, 2012, Levico Terme, Italy.
The first section is focused on Jordan groups in abstract setting,
the second on that in the settings of automorphisms groups and
groups of birational self-maps of algebraic varieties.
The appendix is an expanded version ...
Added: April 28, 2014
Cheltsov I., Kuznetsov A., Shramov K., Algebra & Number Theory 2020 Vol. 14 No. 1 P. 213-274
We construct two small resolutions of singularities of the Coble fourfold (the double cover of the four-dimensional projective space branched over the Igusa quartic). We use them to show that all 𝔖6-invariant three-dimensional quartics are birational to conic bundles over the quintic del Pezzo surface with the discriminant curves from the Wiman–Edge pencil. As an application, ...
Added: May 10, 2020
Przyjalkowski V., Известия РАН. Серия математическая 2013 Т. 77 № 4 С. 135-160
We consider Landau–Ginzburg models for smooth Fano threefolds of the principal series and prove that they can be represented by Laurent polynomials. We check that these models can be compactified to open Calabi–Yau varieties. In the spirit of Katzarkov's programme we prove that the numbers of irreducible components of the central fibres of compactifications of ...
Added: February 6, 2013
Shramov K., Przyjalkowski V., / Cornell University. Series arXiv "math". 2019.
We classify smooth Fano weighted complete intersections of large codimension. ...
Added: November 19, 2019
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017