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In this note, we prove that the holonomy map from the set of equivalence classes of projective structures of parabolic type on non compact surfaces to the set of equivalence classes of parabolic representations of the fundamental group of…
In this paper, we define a new cohomology theory for multiplicative Hom-pre-Lie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one by considering the structure map. We develop…
Hall's binomial rings, rings with binomial coefficients, are given an axiomatisation and proved identical to the numerical rings studied by Ekedahl. The Binomial Transfer Principle is established, enabling combinatorial proofs of…
We investigate the value distribution of holomorphic maps defined on one class of K\"ahler manifolds. With the very natural settings, we establish a Second Main Theorem which is of the similar form as ones of the classical Second Main…
We prove that the set of leaves of a holomorphic lamination of codimension one that are non-transversal to a germ of a holomorphic map is discrete.
We provide a family of isolated tangent to the identity germs $f:(\mathbb{C}^3,0) \to (\mathbb{C}^3,0)$ which possess only degenerate characteristic directions, and for which the lift of $f$ to any modification (with suitable properties)…
We show that the continuous \'etale cohomology groups $H^n_{\mathrm{cont}}(X,\mathbf{Z}_l(n))$ of smooth varieties $X$ over a finite field $k$ are spanned as $\mathbf{Z}_l$-modules by the $n$-th Milnor $K$-sheaf locally for the Zariski…
A complex contact structure $\gamma$ is defined by a system of holomorphic local $1$-forms satisfying the completely non-integrability condition. The contact structure induces a subbundle ${\rm Ker}\, \gamma$ of the tangent bundle and a…
By introducing a new invariant called the set of slidings, we give a complete strict classification of the class of germs of non-dicritical holomorphic foliations in the plan whose Camacho-Sad indices are not rational. Moreover, we will…
This article is devoted to the study of a higher-dimensional generalisation of de Rham epsilon lines. To a holonomic $D$-module $M$ on a smooth variety $X$ and a generic tuple of $1$-form $(\nu_1,\dots,\nu_n)$, we associate a point of the…
We prove an analogue of the de Rham theorem for the extended L^2-cohomology introduced by M. Farber. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of…
We study a germ of real analytic n-dimensional submanifold of $C^n$ that has a complex tangent space of maximal dimension at a CR singularity. Under the condition that its complexification admits the maximum number of deck transformations,…
We show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials…
We construct the $\Lambda$-adic de Rham analogue of Hida's ordinary $\Lambda$-adic \'etale cohomology and of Ohta's $\Lambda$-adic Hodge cohomology, and by exploiting the geometry of integral models of modular curves over the cyclotomic…
Fix a non-negative integer g and a positive integer I dividing 2g-2. For any Henselian, discretely valued field K whose residue field is perfect and admits a degree I cyclic extension, we construct a curve C over K of genus g and index I.…
We prove a rigidity theorem for dominated H\"{o}lder cocycles with values on diffeomorphism groups of a compact manifold over hyperbolic homeomorphisms. More precisely, we show that if two such cocycles have equal periodic data, then they…
We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.
We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.
Recent discoveries make it possible to compute the K-theory of certain rings from their cyclic homology and certain versions of their cdh-cohomology. We extend the work of G. Corti\~nas et al. who calculated the K-theory of, in addition to…
We consider (small) algebraic deformations of germs of real-algebraic CR submanifolds in complex space and study the biholomorphic equivalence problem for such deformations. We show that two algebraic deformations of minimal holomorphically…