Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Monin, Leonid"'
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
We study a broad class of polynomial optimization problems whose constraints and objective functions exhibit sparsity patterns. We give two characterizations of the number of critical points to these problems, one as a mixed volume and one as an inte
Externí odkaz:
http://arxiv.org/abs/2308.07765
In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization problems. We design a polyhedral homotopy algorithm that explicitly c
Externí odkaz:
http://arxiv.org/abs/2302.04117
Autor:
Kühne, Lukas, Monin, Leonid
A cosmological polytope is a lattice polytope introduced by Arkani-Hamed, Benincasa, and Postnikov in their study of the wavefunction of the universe in a class of cosmological models. More concretely, they construct a cosmological polytope for any F
Externí odkaz:
http://arxiv.org/abs/2209.08069
Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of Khovanskii bas
Externí odkaz:
http://arxiv.org/abs/2208.08179
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
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:
Duryev, Eduard, Monin, Leonid
Given a pair of translation surfaces it is very difficult to determine whether they are supported on the same algebraic curve. In fact, there are very few examples of such pairs. In this note we present infinitely many examples of finite collections
Externí odkaz:
http://arxiv.org/abs/2104.08920
This paper is devoted to the study of multigraded algebras and multigraded linear series. For an $\mathbb{N}^s$-graded algebra $A$, we define and study its volume function $F_A:\mathbb{N}_+^s\to \mathbb{R}$, which computes the asymptotics of the Hilb
Externí odkaz:
http://arxiv.org/abs/2104.05397