Related papers: Efficiently and Effectively Recognizing Toricity o…
Let $S_0$ be a smooth and compact real variety given by a reduced regular sequence of polynomials $f_1, ..., f_p$. This paper is devoted to the algorithmic problem of finding {\em efficiently} a representative point for each connected…
Building models that comply with the invariances inherent to different domains, such as invariance under translation or rotation, is a key aspect of applying machine learning to real world problems like molecular property prediction,…
By the classical result of Milnor and Novikov, the unitary cobordism ring is isomorphic to a graded polynomial ring with countably many generators: $\Omega^U_*\simeq \mathbb Z[a_1,a_2,\dots]$, ${\rm deg}(a_i)=2i$. In this paper we solve a…
We study a model of temporal voting where there is a fixed time horizon, and at each round the voters report their preferences over the available candidates and a single candidate is selected. Prior work has adapted popular notions of…
We propose some new uses of toric variety structures in the study of quantum computation for small radices. In particular, we observe the concurrence of the equivalence classes of quantum states under quantum measurement and the orbits of…
We compute the cohomology rings of smooth real toric varieties and of real toric spaces, which are quotients of real moment-angle complexes by freely acting subgroups of the ambient 2-torus. The differential graded algebra we present is in…
We introduce an elementary method to study the border rank of polynomials and tensors, analogous to the apolarity lemma. This can be used to describe the border rank of all cases uniformly, including those very special ones that resisted a…
We construct an almost perfect obstruction theory of virtual dimension zero on the Quot scheme parametrizing zero-dimensional quotients of a locally free sheaf on a smooth projective $3$-fold. This gives a virtual class in degree zero and…
Toric (or sparse) elimination theory is a framework developped during the last decades to exploit monomial structures in systems of Laurent polynomials. Roughly speaking, this amounts to computing in a \emph{semigroup algebra}, \emph{i.e.}…
Tanaka et al. proposed a type system for verifying functional correctness properties of programs that use arrays and pointer arithmetic. Their system extends ConSORT -- a type system combining fractional ownership and refinement types for…
We introduces a general linear framework that unifies the study of multi-winner voting rules and proportionality axioms, demonstrating that many prominent multi-winner voting rules-including Thiele methods, their sequential variants, and…
The complexity of a quantum state may be closely related to the usefulness of the state for quantum computation. We discuss this link using the tree size of a multiqubit state, a complexity measure that has two noticeable (and, so far,…
In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a polynomial system f $=(f\_1, \ldots, f\_N)\in C[x\_1, \ldots,…
We examine Li's double determinantal varieties in the special case that they are toric. We recover from the general double determinantal varieties case, via a more elementary argument, that they are irreducible and show that toric double…
We investigate Gauss maps of (not necessarily normal) projective toric varieties over an algebraically closed field of arbitrary characteristic. The main results are as follows: (1) The structure of the Gauss map of a toric variety is…
We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen-Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative algebraic geometry,…
In this paper we give an explicit formula for the Riemann-Roch map for singular schemes which are quotients of smooth schemes by diagonalizable groups. As an application we obtain a simple proof of a formula for the Todd class of a…
We prove a combinatorial version of Thom's Isotopy Lemma for projection maps applied to any complex or real toric variety. Our results are constructive and give rise to a method for associating the Whitney strata of the projection to the…
We investigate the computational complexity of various decision problems related to conjugacy in finite inverse semigroups. We describe polynomial-time algorithms for checking if two elements in such a semigroup are ~p conjugate and whether…
Based on an idea in Hironaka's proof of resolution of singularities, we present an algorithmic smoothness test for algebraic varieties. The test is inherently parallel and does not involve the calculation of codimension-sized minors of the…