Related papers: Liftable derivations for generically separably alg…

For a generic degree d smooth map f: N^n -> M^n we introduce its "transverse fundamental group" \pi(f), which reduces to \pi_1(M) in the case where f is a covering, and in general admits a monodromy homomorphism \pi(f) -> S_{|d|};…

Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We describe relations between singular complex analytic vector fields…

We investigate a scheme-theoretic variant of Whitney condition a. If X is a projec-tive variety over the field of complex numbers and Y $\subset$ X a subvariety, then X satisfies generically the scheme-theoretic Whitney condition a along Y…

We consider the derivative $D\pi$ of the projection $\pi$ from a stratum of Abelian or quadratic differentials to Teichm\"uller space. A closed one-form $\eta$ determines a relative cohomology class $[\eta]_\Sigma$, which is a tangent…

We study the problem of lifting of polynomial symplectomorphisms in characteristic zero to automorphisms of the Weyl algebra by means of approximation by tame automorphisms. We utilize -- and reprove -- D. Anick's fundamental result on…

We slightly extend the notion of a natural fibre bundle by requiring diffeomorphisms of the base to lift to automorphisms of the bundle only infinitesimally, i.e. at the level of the Lie algebra of vector fields. Spin structures are natural…

We prove that the tangent complex of K-theory, in terms of (abelian) deformation problems over a characteristic 0 field k, is cyclic homology (over k). This equivalence is compatible with the $\lambda$-operations. In particular, the…

In order to have cohomological operations for de Rham p-adic cohomology with coefficients as manageable as possible, the main purpose of this paper is to solve intrinsically and from a cohomological point of view the lifting problem of…

Let $F/\mathbb{Q}$ be a totally real field and $A$ a modular $\GL_2$-type abelian variety over $F$. Let $K/F$ be a CM quadratic extension. Let $\chi$ be a class group character over $K$ such that the Rankin-Selberg convolution $L(s,A,\chi)$…

The purpose of this paper is to explore the geometry and establish the slope stability of tautological vector bundles on Hilbert schemes of points on smooth surfaces. By establishing stability in general we complete a series of results of…

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…

It is shown that if a finite generically smooth morphism $f\,:\,Y\,\longrightarrow\, X$ of smooth projective varieties induces an isomorphism of the \'etale fundamental groups, then the induced map of the stratified fundamental groups…

Let $\Gamma$ be a $d$-flag sortable simplicial complex. We consider the toric ring $R_{\Gamma}=K[{\bf x}_Ft:F\in \Gamma]$ and the Rees algebra of the facet ideals $I(\Gamma^{[i]})$ of pure skeletons of $\Gamma$. We show that these algebras…

Let $S$ be an integral domain with field of fractions $F$ and let $A$ be an $F$-algebra. An $S$-subalgebra $R$ of $A$ is called $S$-nice if $R$ is lying over $S$ and the localization of $R$ with respect to $S \setminus \{ 0 \}$ is $A$. Let…

We consider the set of forms of a toric variety over an arbitrary field: those varieties which become isomorphic to a toric variety after base field extension. In contrast to most previous work, we also consider arbitrary isomorphisms…

Let $p>5$ be a prime integer and $K/\mathbb{Q}_p$ a finite ramified extension with ring of integers $\mathcal{O}$ and uniformizer $\pi$. Let $n>1$ be a positive integer and $\rho_n:G_\mathbb{Q} \to \text{GL}_2(\mathcal{O}/\pi^n)$ be a…

In this paper, we first study the lifting problem of Hasse-Schmidt derivations and then apply the results to the theory of locally trivial deformations of algebraic schemes in positive characteristic. As an application, we construct an…

Using the notion of order convergent nets, we develop an order-theoretic approach to differentiable functions on Archimedean complex $\Phi$-algebras. Most notably, we improve the Cauchy-Hadamard formulas for universally complete complex…

We investigate the positivity and extension of invertible sheaves on group homogeneous spaces over coherent bases. Bypassing the failure of standard limit arguments and the classical Weil--Cartier correspondence, we develop a valuative…

In this paper we prove that both complete and vertical lifts of a Poisson vector field from a Poisson manifold $(M, \pi)$ to its tangent bundle $(TM, \pi_{TM})$ are also Poisson. We use this fact to describe the infinitesimal deformations…