Related papers: Families of surfaces lying in a null set

A finite set $X$ in a Euclidean space $\mathbb{R}^d$ is called Ramsey if for every $k$ there exists an integer $n$ such that whenever $\mathbb{R}^n$ is coloured with $k$ colours, there is a monochromatic copy of $X$. Graham conjectured that…

Let $\Sigma_{g,p}$ be an orientable surface of genus $g$ and of finite type without boundary (i.e. an orientable closed surface with a finite number $p$ of points removed). In this paper we study the R$_{\infty}$-property for the surface…

Let $x$ denote a Laver real over $L$. We prove that in $L[x]$ there is a $\Pi^1_1$ infinite mad family. Since $\Pi^1_1$ and $\Sigma^1_2$ sets are Laver measurable in $L[x]$, this shows that there are examples of well-behaved classical…

We prove smoothness in the dg sense of the bounded derived category of finitely generated modules over any finite-dimensional algebra over a perfect field, hereby answering a question of Iyama. More generally, we prove this statement for…

We investigate the Weyl tensor algebraic structure of a fully general family of D-dimensional geometries that admit a non-twisting and shear-free null vector field k. From the coordinate components of the curvature tensor we explicitly…

Sard's theorem asserts that the set of critical values of a smooth map from one Euclidean space to another one has measure zero. A version of this result for infinite-dimensional Banach manifolds was proven by Smale for maps with Fredholm…

A generic polynomial f(x,y,z) with a prescribed Newton polytope defines a symmetric spatial curve f(x,y,z)=f(y,x,z)=0. We study its geometry: the number, degree and genus of its irreducible components, the number and type of singularities,…

Bauer and Catanese \cite{bauercat} have found 4 families of surfaces of general type with $p_g = q = 0$ which are quotients of the product of curves by the action of finite abelian group. We compute integral homology groups of these…

Given a smooth complex surface S, and a compact connected global normal crossings divisor $D = \cup_i D_i$, we consider the local fundamental group, i.e., the fundamental group Gamma of T-D, where T is a good tubular neighbourhood of D. One…

Let $x=t^n$, $y=\sum_{i=1}^{\infty}a_it^i$ be a parametrisation of the germ of a complex plane analytic curve $\Gamma$ at the origin. Then $\Gamma$ has the implicit equation $f(x,y)=0$ in the neighbourhood of the origin, where $f=\sum…

For certain actions of the Weyl groupoid $\mathfrak{W}$ from [Sergeev and Veselov, Grothendieck rings of basic classical Lie superalgebras, Ann Math, 2011] on an affine variety $X$, geometric properties of the map $\pi: X \longrightarrow Y=…

The existence of smooth families of Lorenz maps exhibiting all possible dynamical behavior is established and the structure of the parameter space of these families is described.

Let Y and X denote C^k vector fields on a possibly noncompact surface with empty boundary, k >0. Say that Y tracks X if the dynamical system it generates locally permutes integral curves of X. Let K be a locally maximal compact set of…

We give a new characterization of a continuous embedding between two function spaces of type $G\Gamma$. Such spaces are governed by functionals of type \begin{equation*} \|f\|_{G\Gamma(r,q;w,\delta)} := \left(\int_{0}^{L} \left(…

We consider Schr\"odinger operators in $L^2(\mathrm{R}^\nu),\, \nu=2,3$, with the interaction in the form on an array of potential wells, each on them having rotational symmetry, arranged along a curve $\Gamma$. We prove that if $\Gamma$ is…

We construct a new family of minimal smooth surfaces of general type with K^2=7 and p_g= 0. We show that for a surface in this family, its canonical divisor is ample and its bicanonical morphism is birational. We prove that these surfaces…

We call every complex connected (1,1)-dimensional supermanifold a super Riemann surface and construct versal super families of compact ones, where the base spaces are allowed to be certain ringed spaces including all complex supermanifolds.…

For a commutative semigroup $S$ with 0, the zero-divisor graph of $S$ denoted by $\Gamma(S)$ is the graph whose vertices are nonzero zero-divisor of $S$, and two vertices $x$, $y$ are adjacent in case $xy=0$ in $S$. In this paper we study…

We completely characterize generalized Young measures generated by sequences of gradients of maps from $W^{1,1}(\Omega;\R^M)$ where $\Omega\subset\R^N$. This extends and completes previous analysis by Kristensen and Rindler where…

Let $\Gamma=(X,\mathcal{R})$ denote a finite, simple, connected, and undirected non-bipartite graph with vertex set $X$ and edge set $\mathcal{R}$. Fix a vertex $x \in X$, and define $\mathcal{R}_f = \mathcal{R} \setminus \{yz \mid…