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Chern classes of reductive groups and an adjunction formula
Annales de l'Institut Fourier. 2006. Vol. 56. No. 4. P. 1225-1256.
In this paper, I construct noncompact analogs of the Chern classes of equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the Euler characteristic of complete intersections in reductive groups. When a complete intersection is a curve, this formula gives an explicit answer for the Euler characteristic and the genus of the curve. An extension of these results to arbitrary spherical homogeneous spaces is outlined. This is the first step towards extension to the reductive case of the explicit answer given by D.Bernstein, Khovanskii and Kouchnirenko for the Euler characteristic of all complete intersections in the complex torus (C^*)^n.
Research target:
Mathematics
Language:
English
Kruglov V., Таланова Г. Н., Журнал Средневолжского математического общества 2017 Т. 19 № 3 С. 31-40
In this paper 2n-gons and surfaces obtained through identification of 2n-gon's sides in pairs (i.e. through sewing) are considered. As well-known, one can get surface of any genus and orientability through sewing but it's very uneasy to calculate by only the polygon and the way of sewing, because to do this one need to calculate ...
Added: November 30, 2017
Smirnov E., Journal of Mathematical Sciences 2020 Vol. 248 No. 3 P. 338-373
This paper is a review of results on multiple flag varieties, i.e., varieties of the form G/P1×· · ·×G/Pr. We provide a classification of multiple flag varieties of complexity 0 and 1 and results on the combinatorics and geometry of B-orbits and their closures in double cominuscule flag varieties. We also discuss questions of finiteness for the ...
Added: July 6, 2020
Kiritchenko Valentina, Krishna A., Transformation Groups 2013 Vol. 18 No. 2 P. 391-413
We obtain an explicit presentation for the equivariant cobordism ring of a complete flag variety. An immediate corollary is a Borel presentation for the ordinary cobordism ring. Another application is an equivariant Schubert calculus in cobordism. We also describe the rational equivariant cobordism rings of wonderful symmetric varieties of minimal rank. ...
Added: February 18, 2013
С. М. Гусейн-Заде, Труды Математического института им. В.А. Стеклова РАН 2022 Т. 318 С. 66-72
Хорошо известная формула для эйлеровой характеристики полного пересечения в комплексном торе в терминах носителей многочленов Лорана — левых частей уравнений, задающих полное пересечение (фактически в терминах выпуклых оболочек носителей — многогранников Ньютона), была анонсирована в краткой заметке Д.Н. Бернштейна, А.Г. Кушниренко и А.Г. Хованского (1976). Её доказательство было дано А.Г. Хованским (1978), но было несамозамкнутым (существенно опиралось на результаты работы другого ...
Added: November 3, 2022
Zhgoon V., Journal of Lie Theory 2013 Vol. 23 P. 607-638
Let $G$ be a connected reductive group acting on an irreducible normal algebraic variety $X$. We give a slightly improved version of Local Structure Theorems obtained by Knop and Timashev, which describe the action of some parabolic subgroup of $G$ on an open subset of $X$. We also extend various results of Vinberg and Timashev ...
Added: February 6, 2013
Terentiuk G., / Cornell University. Series arXiv "math". 2019.
Motivated by the Chern-Weil theory, we prove that for a given vector bundle E on a smooth scheme X over a field k of any characteristic, the Chern classes of E in the Hodge cohomology can be recovered from the Atiyah class. Although this problem was solved by Illusie in \cite{i}, we present another proof by means of derived algebraic geometry.
Also, for a ...
Added: November 20, 2019
Aleksei Golota, / Cornell University. Series arXiv "math". 2019.
For a polarized variety (X,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,−KX) 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 large groups of ...
Added: October 7, 2019
Altmann K., Kiritchenko V., Petersen L., Michigan Mathematical Journal 2015 Vol. 64 P. 3-38
Given a spherical homogeneous space G/H of minimal rank, we provide a simple procedure to describe its embeddings as varieties with torus action in terms of divisorial fans. The torus in question is obtained as the identity component of the quotient group N/H, where N is the normalizer of H in G. The resulting Chow ...
Added: April 3, 2015
R. S. Avdeev, V. S. Zhgoon, Doklady Mathematics 2022 Vol. 105 No. 2 P. 51-55
Let X be an irreducible affine algebraic variety that is spherical with respect to an action of a connected reductive group G. In this paper, we provide sufficient conditions, formulated in terms of weight combinatorics, for the existence of one-parameter additive actions on X normalized by a Borel subgroup B⊂G. As an application, we prove ...
Added: December 8, 2022
Smirnov E., В кн. : Труды семинара по алгебре и геометрии Самарского университета. Т. 147.: М. : ВИНИТИ РАН, 2018. Гл. 3. С. 84-119.
Работа посвящена обзору основных результатов о кратных многообразиях флагов. Приведена классификация кратных многообразий флагов сложности 0 и 1 и изложены результаты о комбинаторике и геометрии B-орбит и их замыканий в двойных комикровесовых многообразиях флагов. Также обсуждаются вопросы конечности числа G-орбит на кратном многообразии флагов и существования на нем открытой G-орбиты. ...
Added: August 19, 2018
Limonchenko I., Лю Ж., Панов Т. Е., Труды Математического института им. В.А. Стеклова РАН 2018 Т. 302 С. 287-295
V. V. Batyrev constructed a family of Calabi–Yau hypersurfaces dual to the first Chern class in toric Fano varieties. Using this construction, we introduce a family of Calabi–Yau manifolds whose SU-bordism classes generate the special unitary bordism ring. We also describe explicit Calabi–Yau representatives for multiplicative generators of the SU-bordism ring in low dimensions. ...
Added: September 25, 2019
Natanzon S. M., М. : МЦНМО, 2018
Bundles, bundles, and their invariants are fundamental concepts of modern geometry that make it possible to investigate the global properties of manifolds ...
Added: March 15, 2018
M. Brion, R. Devyatov, D. Fratila et al., , in : Highlights in Lie Algebraic Methods. : Dordrecht, L., Heidelberg, NY : Birkhäuser, 2012. P. 3-24.
The present constitutes the lecture notes from a mini course at the Summer School ”Structures in Lie Representation Theory” from Bremen in August 2009.
The aim of these lectures is to describe algebraic varieties on which an algebraic group acts and the orbit structure is simple. The methods that will be used come from algebraic geometry, ...
Added: June 27, 2012
Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016
The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...
Added: November 2, 2016
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253
Added: December 22, 2016
Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.
We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...
Added: September 29, 2019
Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.
We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...
Added: March 9, 2014
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
Added: November 1, 2019
Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
Added: August 27, 2016
Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283-291
The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...
Added: December 7, 2013
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
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
Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293
Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...
Added: September 29, 2014