相关论文: Quasi-Homogeneous Linear Systems on P^2 with Base …

In this paper we prove that the generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes of points in the plane has a beautiful decomposition into an infinite product. We also compute the generating series of the…

We give a simple presentation of the six quaternionic equiangular lines in $\mathbb{H}^2$ as an orbit of the primitive quaternionic reflection group of order 720 (which is isomorphic to 2.A_6 the double cover of $A_6)$. Other orbits of this…

We prove that any quasirandom uniform hypergraph $H$ can be approximately decomposed into any collection of bounded degree hypergraphs with almost as many edges. In fact, our results also apply to multipartite hypergraphs and even to the…

Pfister and Steenbrink studied punctual Hilbert schemes for irreducible curve singularities. In particular, they investigated the structure of special punctual Hilbert schemes for certain monomial curve singularities. In this paper, we…

We prove that the Hilbert scheme of points on a normal quasi-projective surface with at worst rational double point singularities is irreducible.

We prove some new semi-finite forms of bilateral basic hypergeometric series. One of them yields in a direct limit Bailey's celebrated ${}_6\psi_6$ summation formula, answering a question recently raised by Chen and Fu ({\em Semi-Finite…

This paper continues our investigation of the dynamics of polynomial diffeomorphisms of C^2. We introduce a dynamical property of polynomial diffeomorphisms that generalizes hyperbolicity in the way that semi-hyperbolicity generalizes…

We study del Pezzo surfaces of degree 1 of the form w^2 = z^3 + Ax^6 + By^6 in the weighted projective space P_k(1,1,2,3), where k is a perfect field of characteristic not 2 or 3 and A,B \in k^*. Over a number field, we exhibit an infinite…

We define naturally Hermite-Lorentz metrics on almost-complex manifolds as special case of pseudo-Riemannian metrics compatible with the almost complex structure. We study their isometry groups.

We construct families of hyperbolic hypersurfaces of degree $2n$ in the projective space $\mathbb{P}^n(\mathbb{C})$ for $3 \leq n \leq 6$.

We apply a heuristic method based on counting points over finite fields to the Poincar\'e center problem. We show that this method gives the correct results for homogeneous non linearities of degree 2 and 3. Also we obtain new evidence for…

A characteristic polynomial is an important invariant in the field of hyperplane arrangement. For the Linial arrangement of any irreducible root system, Postnikov and Stanley conjectured that all roots of the characteristic polynomial have…

In this paper we prove a local well-posedness result for a class of quasi-linear systems of hyperbolic type involving Fourier multipliers. Among the physically relevant systems in this class is a family of Whitham-Boussinesq systems arising…

We derive explicit isomorphisms between certain congruence subgroups of the Siegel modular group, the Hermitian modular group over an arbitrary imaginary-quadratic number field and the modular group over the Hurwitz quaternions of degree 2…

The aim of this paper is twofold: First we classify all abstract light dual multinets of order $6$ which have a unique line of length at least two. Then we classify the weak projective embeddings of these objects in projective planes over…

In this paper, we introduce the concept of completely linear degeneracy for quasilinear hyperbolic systems in several space variables, and then get an interesting property for multidimensional hyperbolic conservation laws. Some examples and…

We prove discrete Helly-type theorems for pseudohalfplanes, which extend recent results of Jensen, Joshi and Ray about halfplanes. Among others we show that given a family of pseudohalfplanes $\cal H$ and a set of points $P$, if every…

Let $\K$ be a field and $(f_1, \ldots, f_n)\subset \K[X_1, \ldots, X_n]$ be a sequence of quasi-homogeneous polynomials of respective weighted degrees $(d_1, \ldots, d_n)$ w.r.t a system of weights $(w_{1},\dots,w_{n})$. Such systems are…

We determine all affinely homogeneous hypersurfaces S^3 in R^4 whose Hessian is (invariantly) of constant rank 2, including the simply transitive ones. We find 34 inequivalent terminal branches yielding each to a nonempty moduli space of…

We prove there are exactly 16 arithmetic lattices of hyperbolic 3-space which are generated by two elements of finite orders p and q with p,q at least six. We also verify a conjecture of H.M. Hilden, M.T. Lozano, and J.M. Montesinos…