Related papers: Classifying codimension 2 multigerms

The theory of algebras with polynomial identities has developed significantly, with special attention devoted to the classification of varieties according to the asymptotic behavior of their codimension sequences. This sequence is a…

Higher order cohomology of arithmetic groups is expressed in terms of (g,K)-cohomology. Generalizing results of Borel, it is shown that the latter can be computed using functions of (uniform) moderate growth. A higher order versions of…

Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…

In this paper we consider a well-known construction due to Gromov and Lawson, Schoen and Yau, Gajer, and Walsh which allows for the extension of a metric of positive scalar curvature over the trace of a surgery in codimension at least $3$…

We prove a stratification result for certain families of $n$-dimensional (complete algebraic) multiplicative character sums. The character sums we consider are sums of products of $r$ multiplicative characters evaluated at rational…

We construct explicit polynomial realizations of some combinatorial Hopf algebras based on various kind of trees or forests, and some more general classes of graphs, ranging from the Connes-Kreimer algebra to an algebra of labelled forests…

We describe some new general constructions of $p$-adic $L$-functions attached to certain arithmetically defined complex $L$-functions coming from motives over $\bold Q$ with coefficiens in a number field $T$, with $[T:\bold Q]<\infty$.…

Let $1\leq p\leq n$ be two positive integers. For a linearly nondegenerate holomorphic mapping $f\colon\mathbb{C}^p\rightarrow\mathbb{P}^n(\mathbb{C})$ of maximal rank intersecting a family of hyperplanes in general position, we obtain a…

Raymond and Wiliams constructed an action of the p-adic integers on an n-dimensional compactum, n>1, with the orbit space of dimension n+2. The author earlier presented a simplified approach for constructing such an action. In this paper we…

Parafermions of order two and three are shown to be the fundamental tool to construct superspaces related to cubic and quartic extensions of the Poincar\'e algebra. The corresponding superfields are constructed, and some of their main…

We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…

Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of…

In this article we derive a complete classification of all submanifolds in space forms with codimension two for which the Gauss map is homothetic.

In order to classify concordance classes of codimension 2 embeddings in a manifold M, we need to determine the complement of such an embedding. These complements are spaces over M well defined up to some homology equivalence. We construct a…

We give the first examples of finitely determined map-germs of corank 3 defined from 3-space to 4-space. We show that they support Mond's conjecture which states that the image Milnor number is greater than or equal to…

By means of a generalization of the Maurer-Cartan expansion method we construct a procedure to obtain expanded higher-order Lie algebras. The expanded higher order Maurer-Cartan equations for the case $\mathcal{G}=V_{0}\oplus V_{1}$ are…

Starting from any unital colored PROP $P$, we define a category $P(P)$ of shapes called $P$-propertopes. Presheaves on $P(P)$ are called $P$-propertopic sets. For $0 \leq n \leq \infty$ we define and study $n$-time categorified $P$-algebras…

In this paper we construct, for every n, smooth varieties of general type of dimension n with the first $\lfloor \frac{n-2}{3} \rfloor$ plurigenera equal to zero. Hacon-McKernan, Takayama and Tsuji have recently shown that there are numbers…

Let $k$ be a field and $V$ an $k$-vector space. For a family $\bar P=\{ P_i\}_{1\leq i\leq c}, $ of polynomials on $V$, we denote by $\mathbb X _{\bar P}\subset V$ the subscheme defined by the ideal generated by $ \bar P$. We show the…

Coarse geometry, and in particular coarse homotopy theory, has proven to be a powerful tool for approaching problems in geometric group theory and higher index theory. In this paper, we continue to develop theory in this area by proving a…