相关论文: The $4n^2$-inequality for complete intersection si…

We give a complete proof of the so called $8n^2$-inequality, a local inequality for the self-intersection of a movable linear system at an isolated centre of a non canonical singularity. The inequality was suggested and several times…

For $\mu$ given latin squares of order $n$, they have {\sf $k$ intersection} when they have $k$ identical cells and $n^2-k$ cells with mutually different entries. For each $n\geq 1$ the set of integers $k$ such that there exist $\mu$ latin…

We show that the variable cohomology of a general complete intersection of quadrics can be identified with the intersection cohomology of a double covering. As a consequence, we show that the middle cohomology of a general complete…

We address the conjecture of [Durfee1978], bounding the singularity genus, p_g, by a multiple of the Milnor number, \mu, for an n-dimensional isolated complete intersection singularity. We show that the original conjecture of Durfee, namely…

A linear system of plane curves satisfying multiplicity conditions at points in general position is called special if the dimension is larger than the expected dimension. A (-1) curve is an irreducible curve with self intersection -1 and…

This is essentially an erratum, with some example to indicate inconsistencies. Suppose $A=k[X_1, X_2, \ldots, X_n]$ is a polynomial ring over a field $k$. The Complete Intersection conjecture states that, for any ideal $I$ in $A$,…

We show that the number of entire maximal graphs with finitely many singular points that are conformally equivalent is a universal constant that depends only on the number of singularities, namely 2^$ for graphs with n+1 singularities. We…

We compute analytically the multi-particle eccentricities, \epsilon_m {2n}, for systems dominated by fluctuations, such as proton-nucleus collisions at the Large Hadron Collider. In particular, we derive a general relation for…

We generalize the Khinchin singularity phenomenon for the problem when, for a given irrational linear subspace, we are looking for rational subspaces that form the smallest angle with the given

Global N=2 supersymmetry in four dimensions with a gauged central charge is formulated in superspace. To find an irreducible representation of supersymmetry for the gauge connections a set of constraints is given. Then the Bianchi…

Given a set $X\subseteq\mathbb{R}^2$ of $n$ points and a distance $d>0$, the multiplicity of $d$ is the number of times the distance $d$ appears between points in $X$. Let $a_1(X) \geq a_2(X) \geq \cdots \geq a_m(X)$ denote the…

We provide a novel proof of the homological excess intersection formula for local complete intersections. The novelty is that the proof makes use of global morphisms comparing the intersections to a self intersection.

Recently a notion of self-duality for differential equations of maximal cuts was introduced, which states that there should be a basis in which the matrix for an {\epsilon}-factorised differential equation is persymmetric. It was observed…

We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…

We prove some inequalities involving fourth central moment of a random variable that takes values in a given finite interval. Both discrete and continuous cases are considered. Bounds for the spread are obtained when a given nxn complex…

We revisit the study of the maximally singular point in the Coulomb branch of 4d N=2 SU(N) gauge theory with N_f=2n flavors for N_f<2N. When n >= 2, we find that the low-energy physics is described by two non-trivial superconformal field…

We collect some classical results about holomorphic 1-forms of a reduced complex curve singularity. They are used to study the pull-back of holomorphic 1-forms on an isolated complete intersection curve singularity under the normalization…

In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…

We investigate $N$-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer $n$, $N=2n+1$ supercharges are explicitly constructed in terms of discrete transformations, and a class of…

We generalize two classical formulas for complete intersection curves by introducing the the complete intersection discrepancy of a curve as a correction term. The first is a well-known multiplicity formula in singularity theory, due to…