Related papers: On Oda's Strong Factorization Conjecture
We study the topology of toric maps. We show that if $f\colon X\to Y$ is a proper toric morphism, with $X$ simplicial, then the cohomology of every fiber of $f$ is pure and of Hodge-Tate type. When the map is a fibration, we give an…
Tensors are ubiquitous in science and engineering and tensor factorization approaches have become important tools for the characterization of higher order structure. Factorizations includes the outer-product rank Canonical Polyadic…
Bernardi and Tirabassi show the existence of full strong exceptional collections consisting of line bundles on smooth toric Fano $3$-folds under assuming Bondal's conjecture, which states that the Frobenius push-forward of the structure…
A general problem in complex cobordism theory is to find useful representatives for cobordism classes. One particularly convenient class of complex manifolds consists of smooth projective toric varieties. The bijective correspondence…
Sonar systems are frequently used to classify objects at a distance by using the structure of the echoes of acoustic waves as a proxy for the object's shape and composition. Traditional synthetic aperture processing is highly effective in…
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…
Recently, a factorization theorem was proposed for partonic flavor evolution as defined by the net flavor of the Winner-Take-All axis of a jet. We validate the factorization theorem through explicit calculation at two-loop order, and in the…
We give an algorithm for removing stackiness from smooth, tame Artin stacks with abelian stabilisers by repeatedly applying stacky blow-ups. The construction works over a general base and is functorial with respect to base change and…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated…
We determine a strong form of the decomposition theorem for proper toric maps over finite fields.
We give a short proof of the Zariski-Lipman conjecture for toric varieties: any complex toric variety with locally free tangent sheaf is smooth.
We study hadronic jets that are tagged as heavy-flavoured, i.e. they contain either beauty or charm. In particular, we consider heavy-flavour jets that have been groomed with the Soft Drop algorithm. In order to achieve a deeper…
Tadao Oda conjectured that every smooth polytope has the Integer Decomposition Property. In this paper, we show this result for a subclass of polytopes: smooth combinatorial cubes of any dimension.
The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…
In this paper, motivated by the theory of operads and PROPs we reveal the combinatorial nature of tensor calculus for strict tensor categories and show that there exists a monad which is described by the coarse-graining of graphs and…
The purpose of this note is to give a simple proof of the following theorem: Let $X$ be a normal projective variety over an algebraically closed field $k$, $\op{char} k = 0$ and let $D \subset X$ be a proper closed subvariety of $X$. Then…
Let $f:X \to Y$ be a proper morphism of normal varieties with $f_*\mathcal{O}_X = \mathcal{O}_Y$. If $X$ is toric, then $Y$ is toric and $f$ is a toric morphism for some toric structures on $X$ and $Y$.
Toda's Theorem is a fundamental result in computational complexity theory, whose proof relies on a reduction from a QBF problem with a constant number of quantifiers to a model counting problem. While this reduction, henceforth called…
A map Y -> P^n is determined by a line bundle quotient of (O_Y)^{n+1}. In this paper, we generalize this description to the case of maps from Y to an arbitrary smooth toric variety. The data needed to determine such a map consists of a…