An L2-Poincaré–Dolbeault lemma of spaces with mixed cone-cusp singular metrics

2021 ◽  
pp. 1-20
Author(s):  
Junchao Shentu ◽  
Chen Zhao
Keyword(s):  
Spectral Sequence ◽  
Einstein Metrics ◽  
Neumann Boundary ◽  
De Rham Cohomology ◽  
Hodge Structures ◽  
Geometric Invariants ◽  
Singular Metrics ◽  
De Rham ◽  
Frölicher Spectral Sequence ◽  
Kähler Einstein Metrics

The existence of Kähler Einstein metrics with mixed cone and cusp singularity has received considerable attentions in recent years. It is believed that such kind of metric would give rise to important geometric invariants. We computed their [Formula: see text]-Hodge–Frölicher spectral sequence under the Dirichlet and Neumann boundary conditions and examine the pure Hodge structures on them. It turns out that these cohomologies agree well with the de Rham cohomology of a good compactification.

scholarly journals The serre spectral sequence of a noncommutative fibration for de Rham cohomology

2005 ◽  
Vol 195 (2) ◽  
pp. 155-196 ◽  
Author(s):  
Edwin J. Beggs ◽  
Tamasz Brzeziński
Keyword(s):  
Spectral Sequence ◽  
De Rham Cohomology ◽  
Serre Spectral Sequence ◽  
De Rham

scholarly journals THE VAN EST SPECTRAL SEQUENCE FOR HOPF ALGEBRAS

2004 ◽  
Vol 01 (01n02) ◽  
pp. 33-48 ◽  
Author(s):  
E. J. BEGGS ◽  
TOMASZ BRZEZIŃSKI
Keyword(s):  
Hopf Algebra ◽  
Spectral Sequence ◽  
Lie Algebra ◽  
Hopf Algebras ◽  
Cohomology Group ◽  
Spectral Sequences ◽  
De Rham Cohomology ◽  
Lie Algebra Cohomology ◽  
De Rham ◽  
Definition Of

Various aspects of the de Rham cohomology of Hopf algebras are discussed. In particular, it is shown that the de Rham cohomology of an algebra with the differentiable coaction of a cosemisimple Hopf algebra with trivial 0-th cohomology group, reduces to the de Rham cohomology of (co)invariant forms. Spectral sequences are discussed and the van Est spectral sequence for Hopf algebras is introduced. A definition of Hopf–Lie algebra cohomology is also given.

Mixed Hodge Structures

2017 ◽  
Author(s):  
Fouad El Zein ◽  
Lˆe D˜ung Tr ´ang
Keyword(s):  
Spectral Sequence ◽  
Linear Algebra ◽  
Algebraic Variety ◽  
Spectral Sequences ◽  
Hodge Structures ◽  
De Rham Complex ◽  
Rham Complex ◽  
De Rham ◽  
Definition Of ◽  
Mixed Hodge Structures

This chapter discusses mixed Hodge structures (MHS). It first defines the abstract category of Hodge structures and introduces spectral sequences. The decomposition on the cohomology of Kähler manifolds is used to prove the degeneration at rank 1 of the spectral sequence defined by the filtration F on the de Rham complex in the projective nonsingular case. The chapter then introduces an abstract definition of MHS as an object of interest in linear algebra. It then attempts to develop algebraic homology techniques on filtered complexes up to filtered quasi-isomorphisms of complexes. Finally, this chapter provides the construction of the MHS on any algebraic variety.

A spectral sequence for de Rham cohomology

2011 ◽  
Vol 149 (3) ◽  
pp. 245-263
Author(s):  
Bingyong Xie
Keyword(s):  
Spectral Sequence ◽  
De Rham Cohomology ◽  
De Rham

THE DE RHAM COHOMOLOGY OF DIFFERENTIAL SPACES

1989 ◽  
Vol 22 (1) ◽  
pp. 249-272 ◽  
Author(s):  
Wiesław Sasin
Keyword(s):  
De Rham Cohomology ◽  
De Rham ◽  
Differential Spaces

scholarly journals Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

2017 ◽  
Vol 4 (1) ◽  
pp. 43-72 ◽  
Author(s):  
Martin de Borbon
Keyword(s):  
Vector Field ◽  
Einstein Metrics ◽  
Projective Line ◽  
Tangent Cones ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Complex Curves ◽  
Complex Dimensions ◽  
Irregular Case ◽  
Kähler Einstein Metrics

Abstract The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

scholarly journals Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p

2021 ◽  
Vol 9 ◽  
Author(s):  
Benjamin Antieau ◽  
Bhargav Bhatt ◽  
Akhil Mathew
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Characteristic P ◽  
De Rham

Abstract We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate.

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