Related papers: $N_6$ property for third Veronese embeddings

Let R be the free algebra on x and y modulo the relations x^5=yxy and y^2=xyx endowed with the grading deg x=1 and deg y=2. Let B_3 denote the blow up of the projective plane at three non-colliear points. The main result in this paper is…

We discuss a new companion to Capparelli's identities. Capparelli's identities for m=1,2 state that the number of partitions of $n$ into distinct parts not congruent to m, -m modulo $6$ is equal to the number of partitions of n into…

In this paper we generalize techniques of Belk-Matucci to solve the conjugacy problem for every Thompson-like group $V_n(H)$, where $n \geq 2$ and $H$ is a subgroup of the symmetric group on $n$ elements. We use this to prove that, if $n…

The moduli in a 4D N=1 heterotic compactification on an elliptic CY, as well as in the dual F-theoretic compactification, break into "base" parameters which are even (under the natural involution of the elliptic curves), and "fiber" or…

The naturally topologized order complex of proper algebraic subsets in $RP^2$, defined by systems of quadratic forms, has rational homology of $S^{13}$

This work settles the Eichler-Shimura congruence relation of Blasius and Rogawski for certain 5-dimensional Hodge-type Shimura varieties, that were not tractable by previously known methods. In a more general context we introduce a…

We prove that the cohomology groups with rational coefficients of the Voronoi compactification of the moduli space of abelian threefolds coincide with the Chow groups of that space, as determined by Van der Geer.

J. L. Andersen proved that there is 5-torsion in the bottom nonvanishing homology group of the simplicial complex of graphs of degree at most two on seven vertices. We use this result to demonstrate that there is 5-torsion also in the…

We relate the embeddability of the simplicial complex $[3]*K$ into $\mathbb{R}^{n+2}$ to that of $K$ into $\mathbb{R}^n$. In brief, the embeddability of $K$ into $\mathbb{R}^n$, in the metastable range $2n\geq 3(d+1)$, is equivalent to the…

Let $\Gamma_{0,n}^+(p)\subset \mathrm{SL}_n(\mathbb{Z})$ be the congruence subgroup of level-$p$ whose first column is of the form $(*,0,\dots,0)^t\bmod p$. We prove that the top-dimensional cohomology group…

We show that a pseudo-holomorphic embedding of an almost-complex $2n$-manifold into almost-complex $(2n + 2)$-Euclidean space exists if and only if there is a CR regular embedding of the $2n$-manifold into complex $(n + 1)$-space. We remark…

In this article, we give a condition on the vanishing of finitely many homogeneous components which must imply the asymptotic vanishing for multigraded modules. We apply our result to multi-Rees algebras of ideals. As a consequence, we…

The rational cohomology ring of A_3, the moduli space of abelian 3-folds is computed. This is isomorphic to the the rational cohomology ring of the group Sp_3(Z) of 6x6 integral symplectic matrices. The main ingredients in the computation…

We prove that every finitely presented self-similar group embeds in a finitely presented simple group. This establishes that every group embedding in a finitely presented self-similar group satisfies the Boone-Higman conjecture. The simple…

It was conjectured, twenty years ago, the following result that would generalize the so-called rank rigidity theorem for homogeneous Euclidean submanifolds: let M^n, n>=2, be a full and irreducible homogeneous submanifold of the sphere…

We calculate rational homology groups of spaces of non-resultant (i.e. having no non-trivial common zeros) systems of homogemeous quadratic polynomials in R^3

We prove vanishing results for the coherent cohomology of the good reduction modulo $p$ of the Siegel variety with coefficients in some automorphic bundles. We show that for an automorphic bundle with highest weight $\lambda$ near the walls…

Let $Z$ be a compact, connected $3$-dimensional complex manifold with vanishing first and second Betti numbers and non-vanishing Euler characteristic. We prove that there is no holomorphic mapping from $Z$ onto any $2$-dimensional complex…

In part I we reduced the arithmetic (characteristic zero) version of the P \not \subseteq NP conjecture to the problem of showing that a variety associated with the complexity class NP cannot be embedded in the variety associated the…

We show that uniformly finite homology of products of $n$ trees vanishes in all degrees except degree $n$, where it is infinite dimensional. Our method is geometric and applies to several large scale homology theories, including almost…