scholarly journals Toric foliations with split tangent sheaf

2022 ◽  
pp. 103099
Author(s):  
Sebastián Velazquez
Keyword(s):  
Tangent Sheaf

scholarly journals Flags of holomorphic foliations

2011 ◽  
Vol 83 (3) ◽  
pp. 775-786 ◽  
Author(s):  
Rogério S. Mol
Keyword(s):  
Finite Number ◽  
Complex Manifold ◽  
Necessary Conditions ◽  
Holomorphic Foliations ◽  
Lower Dimension ◽  
Higher Dimension ◽  
Basic Properties ◽  
Codimension One ◽  
Tangent Sheaf ◽  
Polar Classes

A flag of holomorphic foliations on a complex manifold M is an object consisting of a finite number of singular holomorphic foliations on M of growing dimensions such that the tangent sheaf of a fixed foliation is a subsheaf of the tangent sheaf of any of the foliations of higher dimension. We study some basic properties oft hese objects and, in <img src="/img/revistas/aabc/2011nahead/aop2411pcn.jpg" align="absmiddle" />, n > 3, we establish some necessary conditions for a foliation, we find bounds of lower dimension to leave invariant foliations of codimension one. Finally, still in <img src="/img/revistas/aabc/2011nahead/aop2411pcn.jpg" align="absmiddle" /> involving the degrees of polar classes of foliations in a flag.

scholarly journals Semistability of the tangent sheaf of singular varieties

2016 ◽  
Vol 3 (5) ◽  
pp. 508-542 ◽  
Author(s):  
Henri Guenancia
Keyword(s):  
Singular Varieties ◽  
Tangent Sheaf

scholarly journals The Continuous Hochschild Cochain Complex of a Scheme

2002 ◽  
Vol 54 (6) ◽  
pp. 1319-1337 ◽  
Author(s):  
Amnon Yekutieli
Keyword(s):  
Finite Type ◽  
Chain Complex ◽  
Derived Category ◽  
Cochain Complex ◽  
Relative Dimension ◽  
Base Ring ◽  
Tangent Sheaf

AbstractLet X be a separated finite type scheme over a noetherian base ring . There is a complex of topological -modules, called the complete Hochschild chain complex of X. To any -module —not necessarily quasi-coherent—we assign the complex of continuous Hochschild cochains with values in . Our first main result is that when X is smooth over there is a functorial isomorphismin the derived category , where .The second main result is that if X is smooth of relative dimension n and n! is invertible in K, then the standard maps induce a quasi-isomorphismWhen this is the quasi-isomorphism underlying the Kontsevich Formality Theorem.Combining the two results above we deduce a decomposition of the globalHochschild cohomologywhere is the relative tangent sheaf.

scholarly journals Hypersurfaces invariant by Pfaff systems

2015 ◽  
Vol 17 (06) ◽  
pp. 1450051 ◽  
Author(s):  
Maurício Corrêa ◽  
Luis G. Maza ◽  
Márcio G. Soares
Keyword(s):  
First Integrals ◽  
Holomorphic Foliation ◽  
Complex Manifolds ◽  
Arbitrary Codimension ◽  
Tangent Sheaf

We present results expressing conditions for the existence of meromorphic first integrals for Pfaff systems of arbitrary codimension on complex manifolds. Some of the results presented improve previous ones due to Jouanolou and Ghys. We also present an enumerative result counting the number of hypersurfaces invariant by a projective holomorphic foliation with split tangent sheaf.

scholarly journals Smoothing Pairs Over Degenerate Calabi–Yau Varieties

2020 ◽  
Author(s):  
Kwokwai Chan ◽  
Ziming Nikolas Ma
Keyword(s):  
Free Sheaf ◽  
Locally Free Sheaf ◽  
Tangent Sheaf ◽  
Perfect Complex

Abstract We apply the techniques developed in [2] to study smoothings of a pair $(X,\mathfrak{C}^*)$, where $\mathfrak{C}^*$ is a bounded perfect complex of locally free sheaves over a degenerate Calabi–Yau variety $X$. In particular, if $X$ is a projective Calabi–Yau variety admitting the structure of a toroidal crossing space and with the higher tangent sheaf $\mathcal{T}^1_X$ globally generated, and $\mathfrak{F}$ is a locally free sheaf over $X$, then we prove, using the results in [ 8], that the pair $(X,\mathfrak{F})$ is formally smoothable when $\textrm{Ext}^2(\mathfrak{F},\mathfrak{F})_0 = 0$ and $H^2(X,\mathcal{O}_X) = 0$.

ON THE SINGULAR SCHEME OF CODIMENSION ONE HOLOMORPHIC FOLIATIONS IN ℙ3

2010 ◽  
Vol 21 (07) ◽  
pp. 843-858 ◽  
Author(s):  
LUIS GIRALDO ◽  
ANTONIO J. PAN-COLLANTES
Keyword(s):  
Singular Locus ◽  
The Other ◽  
Holomorphic Foliation ◽  
Holomorphic Foliations ◽  
Codimension One ◽  
Other Hand ◽  
Tangent Sheaf ◽  
Torsion Free

In this work, we begin by showing that a holomorphic foliation with singularities is reduced if and only if its normal sheaf is torsion-free. In addition, when the codimension of the singular locus is at least two, it is shown that being reduced is equivalent to the reflexivity of the tangent sheaf. Our main results state on one hand, that the tangent sheaf of a codimension one foliation in ℙ3 is locally free if and only if the singular scheme is a curve, and that it splits if and only if it is arithmetically Cohen–Macaulay. On the other hand, we discuss when a split foliation in ℙ3 is determined by its singular scheme.

scholarly journals Completed tensor products and a global approach to p-adic analytic differential operators

2018 ◽  
Vol 167 (02) ◽  
pp. 389-416
Author(s):  
ANDREAS BODE
Keyword(s):  
Differential Operators ◽  
Tensor Products ◽  
Necessary And Sufficient Condition ◽  
Main Ingredient ◽  
Mixed Characteristic ◽  
Valued Field ◽  
Tangent Sheaf ◽  
Necessary And Sufficient ◽  
Exact Sequences ◽  
Natural Way

AbstractArdakov-Wadsley defined the sheaf $\wideparen{\Ncal{D}}$X of p-adic analytic differential operators on a smooth rigid analytic variety by restricting to the case where X is affinoid and the tangent sheaf admits a smooth Lie lattice. We generalise their results by dropping the assumption of a smooth Lie lattice throughout, which allows us to describe the sections of $\wideparen{\Ncal{D}}$ for arbitrary affinoid subdomains and not just on a suitable base of the topology. The structural results concerning $\wideparen{\Ncal{D}}$ and coadmissible $\wideparen{\Ncal{D}}$-modules can then be generalised in a natural way.The main ingredient for our proofs is a study of completed tensor products over normed K-algebras, for K a discretely valued field of mixed characteristic. Given a normed right module U over a normed K-algebra A, we provide several exactness criteria for the functor $U\widehat{\otimes}_A$ - applied to complexes of strict morphisms, including a necessary and sufficient condition in the case of short exact sequences.

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