Related papers: Abundance theorem for threefolds in mixed characte…

We show that many cluster-theoretic properties of the Markov quiver hold also for adjacency quivers of triangulations of once-punctured closed surfaces of arbitrary genus. Along the way we consider the class P of quivers introduced by…

Over a non-archimedean local field of characteristic zero, we prove the multiplicity preservation for orthogonal-symplectic dual pair correspondences and unitary dual pair correspondences.

We show that any collection of n-dimensional orbifolds with sectional curvature and volume uniformly bounded below, diameter bounded above, and with only isolated singular points contains orbifolds of only finitely many orbifold…

We consider closed acylindrical surfaces in 3-manifolds and in knot and link complements, and show that the genus of these surfaces is bounded linearly by the number of tetrahedra in the triangulation of the manifold and by the number of…

Many questions about triangles and quadrilaterals with rational sides, diagonals and areas can be reduced to solving certain Diophantine equations. We look at a number of such questions including the question of approximating arbitrary…

We prove a quantitative Borg-Levinson theorem for a large class of unbounded potentials. We give a detailed proof when the dimension of the space is greater than or equal to five. We also indicate the modifications necessary to cover lower…

Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with…

We exhibit automorphisms of a certain K3 surface in $\mathbb{P}^1\times \mathbb{P}^1 \times \mathbb{P}^1$ with an isolated fixed point at which the induced action on the stalk of the structure sheaf is arbitrarily close to the identity.…

The aim of this paper is to provide the first application of Theorem 3 of [2] in a case where the dependence of the underlying equation from the real parameter is not of affine type.

This note contains a new proof of a theorem of Gang Xiao saying that the bicanonical map of a surface S of general type is generically finite if and only if the second plurigenus of S is strictly larger than 2. Such properties are also…

This note contains two new observations on the linkage properties of quaternion algebras over fields of characteristic 2: first, that a 3-linked field need not be 4-linked (a case which was left open in previous papers) and that three…

We prove sharp decoupling inequalities for all degenerate surfaces of codimension two in $\mathbb{R}^5$ given by two quadratic forms in three variables. Together with previous work by Demeter, Guo, and Shi in the non-degenerate case…

We are discussing the theorem about the volume of a set $A$ of $Z^n$ having a small doubling property $|2A| < Ck, k=|A|$ and oher problems of Structure Theory of Set Addition (Additive Combinatorics).

We study the polygamy property for tripartite and multipartite quantum systems. In tripartite system, we build a solution set for polygamy in tripartite system and find a lower bound of the set, which can be a sufficient and necessary…

This paper provides closed-form formulas for a multidimensional two-sided matching problem with transferable utility and heterogeneity in tastes. When the matching surplus is quadratic, the marginal distributions of the characteristics are…

In this paper we give the first example of a surface bundle over a surface with at least three fiberings. In fact, for each $n \ge 3$ we construct $4$-manifolds $E$ admitting at least $n$ distinct fiberings $p_i: E \to \Sigma_{g_i}$ as a…

We explicitly find lower bounds on the volume of threefolds and fourfolds of general type in order to have nonvanishing of pluricanonical systems and birationality of pluricanonical maps. In the case of threefolds of large volume, we also…

Let T -> S be a finite flat morphism of degree two between regular integral schemes of dimension at most two (and with 2 invertible), having regular branch divisor D. We establish a bijection between Azumaya quaternion algebras on T and…

In this paper, we study the minimal model theory for threefolds in mixed characteristic. As a generalization of a result of Kawamata, we show that the MMP holds for strictly semi-stable schemes over an excellent Dedekind scheme $V$ of…

We use $q$-binomial theorem to prove three new polynomial identities involving $q$-trinomial coefficients. We then use summation formulas for the $q$-trinomial coefficients to convert our identities into another set of three polynomial…