Related papers: A one-step counterexample to the normalized Nash b…
We discuss an experimental approach to open problems in toric geometry: are smooth projective toric varieties (i) projectively normal and (ii) defined by degree 2 equations? We discuss the creation of lattice polytopes defining smooth toric…
Let $k$ be an infinite finitely generated field of characteristic $p>0$. Fix a separated scheme $X$ smooth, geometrically connected, and of finite type over $k$ and a smooth proper morphism $f:Y\rightarrow X$. The main result of this paper…
In this paper, we give a partial affirmative answer to the BAB conjecture for $3$-folds in characteristic $p>5$. Specifically, we prove that a set $\mathcal{D}$ of weak Fano $3$-folds over an uncountable algebraically closed field is…
We discuss generalizations of the recent theorem by Dafermos (hep-th/0403033) forbidding a certain class of naked singularities in the spherical collapse of a scalar field. Employing techniques similar to the ones Dafermos used, we consider…
We prove that up to automorphisms a line admits a unique embedding into the regular part of of a simplicial toric variety of dimension n>=4 over an algebraically closed field of characteristic zero which is smooth in codimension 2.
In this paper, we establish a Mather-Yau theorem for higher Nash blowup algebras, demonstrating that the isomorphism type of the local ring of any hypersurface singularity, defined over an arbitrary field, is fully determined by its higher…
Let I be an m-primary ideal of a one-dimensional, analytically irreducible and residually rational local Noetherian domain R. Given the blowing-up of R along I we establish connections between the type-sequence of R and classical invariants…
For a polarized toric variety (X,L) of dimension n less than 5, we give a lower bound of the Delta-genus by using the vanishing number of adjoint bundle of a multiple of L. We show that for a polarized toric variety of dimension n with…
A theorem of Esnault, Srinivas and Viehweg asserts that if the Chow group of 0-cycles of a smooth complete complex variety decomposes, then the top-degree coherent cohomology group decomposes similarly. In this note, we prove that (a weak…
We examine the inverse procedure of the Radford-Majid bosonization for Hopf superalgebras and give a handy method for enumerating Hopf superalgebras whose bosonization is isomorphic to a given Hopf algebra. As an application, we classify…
Miyanishi conjecture claims that for any variety over an algebraically closed field of characteristic zero, any endomorphism of such a variety which is injective outside a closed subset of codimension at least $2$ is bijective. We prove…
The purpose of this paper is to give basic tools for the classification of nonsingular toric Fano varieties by means of the notions of primitive collections and primitive relations due to Batyrev. By using them we can easily deal with…
Based on the Monte Carlo kinetic method, we investigated the formation mechanisms of periodical modulations arising along the length of one-dimensional structures. The evolution of initially cylindrical nanowires/slabs at temperatures lower…
This paper classifies toric Fano 3-folds with singular locus { 1/k(1,1,1) } for any positive integer k, building on the work of Batyrev and Watanabe-Watanabe. This is achieved by completing an equivalent problem in the language of Fano…
Given an n-dimensional variety Z with rational singularities, we conjecture that for a resolution of singularities whose reduced exceptional divisor E has simple normal crossings, the (n-1)-th higher direct image of the sheaf of…
We give an explicit regular model for the quadric fibration studied in Pirutka (2011). As an application we show that this construction furnishes a counterexample for the integral Tate conjecture in any odd characteristic for some…
We prove that, for the jet scheme of a singular hypersurface, the blowup of a certain jet-related module is not an isomorphism. In conjunction with recent developments in the theory of Nash blowups, our result holds over fields of arbitrary…
Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field and let $X\to \mathrm{Spec} (A)$ be a resolution of singularity. We prove a theorem giving a condition under which the dimension of the…
An affine algebraic variety X of dimension at least 2 is called flexible if the subgroup SAut(X) in Aut(X) generated by the one-parameter unipotent subgroups acts m-transitively on reg(X) for any m $\ge$ 1. In the previous paper we proved…
In this talk we present the result for the $n_f$ dependent piece of the three-loop cusp anomalous dimension in QCD. Remarkably, it is parametrized by the same simple functions appearing in analogous anomalous dimensions in ${\mathcal N}=4$…