In [2], Billera proved that the R-algebra of continuous piecewise polynomial functions (C0 splines) on a d-dimensional simplicial complex 1 embedded in Rd is a quotient of the Stanley–Reisner ring A1 of 1. We derive a criterion to determine which elements of the Stanley–Reisner ring correspond to splines of higher-order smoothness. In [5], Lau and Stiller point out that the dimension of C k (1)...

then V is a primitive Fano variety of dimensionM , that is, Pic V = ZKV and (−KV ) is ample. The purpose of this note is to sketch a proof of the following Theorem 1. A general (in the sense of Zariski topology) variety V is birationally superrigid. In particular, V admits no non-trivial structures of a rationally connected fibration, any birational map V 99K V ♯ onto a Fano variety with Q-fact...

In this paper we show Whitney’s fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization property along each stratum. We call such a trivial...

We study p-adic families of cohomological automorphic forms for GL(2) over imaginary quadratic fields and prove that interpolating a Zariski-dense set classical cuspidal only occur under very restrictive conditions. show how to computationally determine when this is not the case establish concrete examples finitely many Bianchi modular forms.

variety). For each i, let φi(x) be a C-dense quantifier-free Li-formula with parameters from K. Then we can find a K-definable rational function f : C → P which is non-constant, and has the property that the divisor f−1(0) is a sum of distinct points in ⋂n i=1 φi(K), with no multipliticities. (In particular, the support of the divisor contains no points from C(K)\C(K) and no points from C \ C.)...

Let $R$ be a commutative ring with identity and $M$ be a unitary$R$-module. The primary-like spectrum $Spec_L(M)$ is thecollection of all primary-like submodules $Q$ such that $M/Q$ is aprimeful $R$-module. Here, $M$ is defined to be RSP if $rad(Q)$ isa prime submodule for all $Qin Spec_L(M)$. This class containsthe family of multiplication modules properly. The purpose of thispaper is to intro...

We study the S-integral points on the complement of a union of hyperplanes in projective space, where S is a finite set of places of a number field k. In the classical case where S consists of the set of archimedean places of k, we completely characterize, in terms of the hyperplanes and the field k, when the (S-)integral points are not Zariski-dense.

We study analytic Zariski structures from the point of view of non-elementary model theory. We show how to associate an abstract elementary class with a one-dimensional analytic Zariski structure and prove that the class is stable, quasi-minimal and homogeneous over models. We also demonstrate how Hrushovski’s predimension arises in this general context as a natural geometric notion and use it ...