Zobrazeno 1 - 10
of 519
pro vyhledávání: '"Khovanskii, A."'
Autor:
Khovanskii, Askold, Monin, Leonid
A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an introduction to the
Externí odkaz:
http://arxiv.org/abs/2311.01754
Autor:
Khovanskii, Askold
Publikováno v:
Communications in Mathematics, Volume 31 (2023), Issue 3 (Special issue: in memory of Sergei Duzhin) (January 3, 2024) cm:11527
The notion of center of mass, which is very useful in kinematics, proves to be very handy in geometry (see [1]-[2]). Countless applications of center of mass to geometry go back to Archimedes. Unfortunately, the center of mass cannot be defined for s
Externí odkaz:
http://arxiv.org/abs/2306.15099
Autor:
Khovanskii, Askold
In the paper, we describe all total orders $\succ$ compatible with addition on additive subsemigroup $S$ of finite dimensional spaces over rational numbers. We provide a necessary and sufficient condition under which a finitely generated semigroups $
Externí odkaz:
http://arxiv.org/abs/2210.12835
In this paper we develop a theory of volume polynomials of generalized virtual polytopes based on the study of topology of affine subspace arrangements in a real Euclidean space. We apply this theory to obtain a topological version of the BKK Theorem
Externí odkaz:
http://arxiv.org/abs/2204.00114
We reconsider the theory of Lagrange interpolation polynomials with multiple interpolation points and apply it to linear algebra. For instance, $A$ be a linear operator satisfying a degree $n$ polynomial equation $P(A)=0$. One can see that the evalua
Externí odkaz:
http://arxiv.org/abs/2203.01822
The classical BKK theorem computes the intersection number of divisors on toric variety in terms of volumes of corresponding polytopes. It was observed by Pukhlikov and the first author that the BKK theorem leads to a presentation of the cohomology r
Externí odkaz:
http://arxiv.org/abs/2112.14970
Autor:
Khovanskii, Askold, Monin, Leonid
We study commutative algebras with Gorenstein duality, i.e. algebras $A$ equipped with a non-degenerate bilinear pairing such that $\langle ac,b\rangle=\langle a,bc\rangle$ for any $a,b,c\in A$. If an algebra $A$ is Artinian, such pairing exists if a
Externí odkaz:
http://arxiv.org/abs/2106.15562
Autor:
Braverman, M., Buchshtaber, B. M., Gromov, M., Ivrii, V., Kordyukov, Yu. A., Kuchment, P., Maz'ya, V., Novikov, S. P., Sunada, T., Friedlander, L., Khovanskii, A. G.
The article describes the biography and manifold contributions to research in mathematics of Mikhail Aleksandrovich Shubin.
Externí odkaz:
http://arxiv.org/abs/2008.13543
The celebrated BKK Theorem expresses the number of roots of a system of generic Laurent polynomials in terms of the mixed volume of the corresponding system of Newton polytopes.Pukhlikov and the second author noticed that the cohomology ring of smoot
Externí odkaz:
http://arxiv.org/abs/2006.12043
Autor:
Khovanskii, Askold
A new transparent proof of the well known good compactification theorem for the complex torus $(\Bbb C^*)^n$ is presented. This theorem provides a powerful tool in enumerative geometry for subvarieties in the complex torus. The paper also contains an
Externí odkaz:
http://arxiv.org/abs/2002.02069