Related papers: Singular varieties and infinitesimal non-commutati…

We describe all Witt invariants of anti-hermitian forms over a quaternion algebra with its canonical involution, and in particular all Witt invariants of orthogonal groups $O(A,\sigma)$ where $(A,\sigma)$ is an central simple algebra with…

We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let $\pi$ be a unitary, cuspidal, automorphic representation of $GL_n(\A_K)$. Let $S$ be a set of finite places of $K$, such that the sum $\sum_{v\in…

We show a surprising link between singularity theory and the invariant subspace problem of nilpotent operators as recently studied by C. M. Ringel and M. Schmidmeier, a problem with a longstanding history going back to G. Birkhoff. The link…

The modular variety of non singular and complete hyperelliptic curves with level-two structure of genus 3 is a 5-dimensional quasi projective variety which admits several standard compactifications. The first one, X, comes from the…

We study finite and semi-finite vector bundles on complex tori. We give an explicit decomposition of such bundles in terms of torsion and unipotent factors. As a consequence, we prove that the extended Nori fundamental group scheme of a…

In this work, we describe how to obtain the structure of an infinite-dimensional Lie group on the group of compactly carried bundle automorphisms Autc(P) for a locally convex prinicpal bundle P over a finite-dimensional smooth sigma-compact…

It is known that Chern characteristic numbers of compact complex manifolds cannot have arbitrary values. They satisfy certain divisability conditions. W. Ebeling and S. M. Gusein-Zade gave a definition of Chern characteristic numbers of…

For a tuple $A=(A_1,\ A_2,\ ...,\ A_n)$ of elements in a unital algebra ${\mathcal B}$ over $\mathbb{C}$, its {\em projective spectrum} $P(A)$ or $p(A)$ is the collection of $z\in \mathbb{C}^n$, or respectively $z\in \mathbb{P}^{n-1}$ such…

The classical Zariski-van Kampen theorem gives a presentation of the fundamental group of the complement of a complex algebraic curve in $\mathbb{P}^2$. The first generalization of this theorem to singular (quasi-projective) varieties was…

We define Weil spaces, Weil manifolds, Weil varieties and Weil Lie groups over an arbitrary commutative base ring K (in particular, over discrete rings such as the integers), and we develop the basic theory of such spaces, leading up the…

In 1981 J. Wahl described smoothings of surface quotient singularities with no vanishing cycles. Given a smoothing of a projective surface X of this type, we construct an associated exceptional vector bundle on the nearby fiber Y in the…

We study the symplectomorphism groups $G_{\lambda}=Symp_0(M,\omega_{\lambda})$ of an arbitrary closed manifold M equipped with a 1-parameter family of symplectic forms $\omega_{\lambda}$ with variable cohomology class. We show that the…

The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…

To any unramified double cover $\pi:\tilde C \to C$ of projective irreducible and nonsingular curves one associates the Prym variety $P = P(\pi)$. For $C$ nonhyperelliptic of genus $g \geq 6$ we consider the natural embedding $\tilde C…

Let $K$ be a field, $\Gamma $ a finite group of field automorphisms of $K$, $F$ the $\Gamma $-fixed field in $K$ and $G\leq $GL$_v(K)$ a finite matrix group. Then the action of $\Gamma $ defines a grading on the symmetric algebra of the…

Let $f: Y\to X$ be a morphism between smooth complex quasi-projective varieties and $Z$ be the closure of $f(Y)$ with $\iota: Z\to X$ the inclusion map. We prove that a. for any field $K$, there exist finitely many semisimple…

A natural oriented (2k+2)-chain in CP^{2k+1} with boundary twice RP^{2k+1}, its complex shade, is constructed. Via intersection numbers with the shade, a new invariant, the shade number of k-dimensional subvarieties with normal vector…

We describe a multivariable polynomial invariant for certain class of non isolated hypersurface singularities generalizing the characteristic polynomial on monodromy. The starting point is an extension of a theorem due to Le Dung Trang and…

Let $(X, D_{X})$ be an arbitrary pointed stable curve of topological type $(g_{X}, n_{X})$ over an algebraically closed field of characteristic $p>0$. We prove that the generalized Hasse-Witt invariants of prime-to-$p$ cyclic admissible…

Let $X\subseteq \mathbb{P}^N$ be a non-degenerate normal projective variety of codimension $e$ and degree $d$ with isolated $\mathbb{Q}$-Gorenstein singularities. We prove that the Castelnuovo-Mumford regularity…