Related papers: Smooth Gevrey normal forms of vector fields near a…

We study semiclassical Gevrey pseudodifferential operators, acting on exponentially weighted spaces of entire holomorphic functions. The symbols of such operators are Gevrey functions defined on suitable I-Lagrangian submanifolds of the…

The support vector machine (SVM) is a supervised learning algorithm that finds a maximum-margin linear classifier, often after mapping the data to a high-dimensional feature space via the kernel trick. Recent work has demonstrated that in…

Let $k$ be an algebraically closed field of characteristic $p>0$. Let $c,d,m$ be positive integers. Let $D$ be a $p$-divisible group of codimension $c$ and dimension $d$ over $k$. Let $\scrD$ be a versal deformation of $D$ over a smooth…

Given a closed Riemannian manifold $(M^m,g)$ and a vector field $v$ on $M$, we form the Sasaki metric $g_S$ on $TM$, and restrict it to the image of the cross section map of $M$ into $TM$ defined by $v$, whose pull back to $M$ defines a new…

We use the "closed point sieve" to prove a variant of a Bertini theorem over finite fields. Specifically, given a smooth quasi-projective subscheme X of P^n of dimension m over F_q, and a closed subscheme Z in P^n such that Z intersect X is…

The embedded Nash problem for a hypersurface in a smooth algebraic variety, is to characterize geometrically the maximal irreducible families of arcs with fixed order of contact along the hypersurface. We show that divisors on minimal…

Let $X$ be a smooth irreducible projective variety of dimension at least 2 over an algebraically closed field of characteristic 0 in the projective space ${\mathbb{P}}^n$. Bertini's Theorem states that a general hyperplane $H$ intersects…

Fix a smooth projective family of curves $C \to S$ and a split reductive group scheme $G$ over a Noetherian base scheme $S$. For any (possibly nonreduced) fixed relative Cartier divisor $D$, we provide a treatment of the moduli of…

The present paper concerns the invariants of generically nef vector bundles on ruled surfaces. By Mehta - Ramanathan Restriction Theorem and by Miyaoka characterization of semistable vector bundles on a curve, the generic nefness can be…

For any plane curve singularity defined by an analytic function germ $f$, we construct a spine on each Milnor fiber simultaneously, that realizes the vanishing topology. In order to do so, we study the separatrices at the origin of the…

This note is intended to reformulate the Dixmier-Malliavin theorem about smooth group representations in the language of bornological vector spaces, instead of topological vector spaces. This language turns out to allow a more general…

We discuss algebraic vector bundles on smooth k-schemes X contractible from the standpoint of A^1-homotopy theory; when k = C, the smooth manifolds X(C) are contractible as topological spaces. The integral algebraic K-theory and integral…

In this note the smooth (i.e. with open stabilizers) linear and {\sl semilinear} representations of certain permutation groups (such as infinite symmetric group or automorphism group of an infinite-dimensional vector space over a finite…

The description of the Paley-Wiener space for compactly supported smooth functions $C^\infty_c(G)$ on a semi-simple Lie group $G$ involves certain intertwining conditions that are difficult to handle. In the present paper, we make them…

Let $X$ be a Hamiltonian vector field defined on a symplectic manifold $(M,\omega)$, $g$ a nowhere vanishing smooth function defined on an open dense subset $M^0$ of $M$. We will say that the vector field $Y = gX$ is conformally…

In this note we give an easy proof of the existence of generically smooth components of the expected dimension of certain Brill--Noether loci of stable rank 2 vector bundles on a curve with general moduli, with related applications to…

We prove that certain vector bundles over surfaces are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to $\det(E)$). This result is a higher-rank version of a theorem…

Let X be a smooth complex projective curve of genus g bigger or equal to 1. If g is bigger than 1 assume further that X is either bielliptic or with general moduli. Under a natural condition on slopes, we prove that there exists a short…

A vector-like extension of the standard model for heavier quarks and leptons with $SU(2)\times U(1)$ gauge symmetry and only one Higgs doublet is examined. This scheme incorporates infinitely many fermions and avoids the appearance of a…

It is well known that smooth (or continuous) vector fields cannot be topologically transitive on the sphere $\S^2$. Piecewise-smooth vector fields, on the other hand, may present non-trivial recurrence even on $\S^2$. Accordingly, in this…