Related papers: A new 5-fold flop and derived equivalence
This paper considers affine analogues of the isoperimetric inequality in the sense of piecewise linear topology. Given a closed polygon P embedded in R^d having n edges, we give upper and lower bounds for the minimal number of triangles…
Comparison theorems are foundational to our understanding of the geometric features implied by various curvature constraints. This paper considers manifolds with a positive lower bound on either scalar, 2-Ricci, or Ricci curvature, and…
By Liouville's theorem, in dimensions 3 or more conformal transformations form a finite-dimensional group, an apparent drastic departure from the 2-dimensional case. We propose a derived enhancement of the conformal Lie algebra which is an…
We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for…
This article describes the following results which relate to each other; i) convergence of high dimensional contact structure to codimension one foliation with Reeb component, ii) relation between Nil-type and Sol-type contact submanifolds…
We prove derived equivalence of Calabi-Yau threefolds constructed by Ito-Miura-Okawa-Ueda as an example of non-birational Calabi-Yau varieties whose difference in the Grothendieck ring of varieties is annihilated by the affine line.
We associate two linear categories with two objects to a module over the subalgebra of coinvariants of a Hopf-Galois extension, and prove that they are isomorphic. The structure Theorem for cleft extensions, and the Militaru \cStefan…
Five dimensional super conformal field theories can be studied using their geometric realisation as a limit of $M$-theory on a metrically conical Calabi-Yau threefold. We utilise this framework to investigate the phases of such theories…
Given a nilpotent Lie algebra, we study the space of all diagonalizable derivations such that the corresponding one-dimensional solvable extension admits a left-invariant metric with negative Ricci curvature. It has been conjectured by…
Mixed $f$-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are…
It is shown that Nichols algebras over alternating groups A_m, m>4, are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes isomorphic to A_m is isomorphic to the group…
An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note,…
We give an inequality of type sup x inf in dimension 5 for a Yamabe type equation.
We show that the graded Chow rings of two birational irreducible symplectic varieties are isomorphic. This lifts a result known for the cohomology algebras to the level of Chow rings, despite the non-injectivity the cycle class map. In the…
We prove two results about transforming any convex polyhedron, modeled as a linkage L of its edges. First, if we subdivide each edge of L in half, then L can be continuously flattened into a plane. Second, if L is equilateral and we again…
For a Cohen-Macaulay ring $R$, we exhibit the equivalence of the bounded derived categories of certain resolving subcategories, which, amongst other results, yields an equivalence of the bounded derived category of finite length and finite…
Calabi-Yau threefolds with infinitely many flops to isomorphic manifolds have an extended Kahler cone made up from an infinite number of individual Kahler cones. These cones are related by reflection symmetries across flop walls. We study…
The equality constraint a+b+c=1 for random triangle sides corresponds to breaking a stick in two places. An analog a^2+b^2+c^2=1 has a remarkable feature: the bivariate density for angles coincides with that for 3D Gaussian triangles.…
We give a counterexample to a recently conjectured variant of the Penrose inequality.
We give a complete classification of the 32-dimensional pointed Hopf algebras over an algebraically closed field k with characteristic different from 2. It turns out that there are infinite families of isomorphism classes of pointed Hopf…