Locally free sheaves on complex supermanifolds

Onishchik, A. L.; Vishnyakova, Elizaveta

doi:10.1007/s00031-013-9219-8

Cited by 9 publications

(10 citation statements)

References 18 publications

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“…This paper is based on the paper [3], where two classification theorems for locally free sheaves on supermanifolds were proved and a spectral sequence for a locally free sheaf of modules E was obtained. We consider another filtration of the locally free sheaf E , the corresponding classification theorem and the spectral sequence, which is more convenient in some cases.…”

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confidence: 99%

“…We consider another filtration of the locally free sheaf E , the corresponding classification theorem and the spectral sequence, which is more convenient in some cases. The methods, which we are using here, are similar to [2,3].The first spectral sequence of this kind was constructed by A.L. Onishchik in [2] for the tangent sheaf of a supermanifold.…”

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confidence: 99%

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confidence: 99%

“…Unlike the Z 2 -grading considered in [3], the natural Z 2 -grading is compatible with this Z-grading.…”

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confidence: 99%

“…The spectral sequence 2.1. Quasi-derivations Quasi-derivations were defined in [3]. Let us briefly recall that construction.…”

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confidence: 99%

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A Classification Theorem and a Spectral Sequence for a Locally Free Sheaf Cohomology of a Supermanifold

Vishnyakova

2012

Geometric Methods in Physics

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Abstract. This paper is based on the paper [3], where two classification theorems for locally free sheaves on supermanifolds were proved and a spectral sequence for a locally free sheaf of modules E was obtained. We consider another filtration of the locally free sheaf E , the corresponding classification theorem and the spectral sequence, which is more convenient in some cases. The methods, which we are using here, are similar to [2,3].The first spectral sequence of this kind was constructed by A.L. Onishchik in [2] for the tangent sheaf of a supermanifold. However, the spectral sequence considered in this paper is not a generalization of Onishchik's spectral sequence from [2].

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confidence: 99%

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confidence: 99%

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confidence: 99%

“…Unlike the Z 2 -grading considered in [3], the natural Z 2 -grading is compatible with this Z-grading.…”

mentioning

confidence: 99%

“…The spectral sequence 2.1. Quasi-derivations Quasi-derivations were defined in [3]. Let us briefly recall that construction.…”

mentioning

confidence: 99%

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A Classification Theorem and a Spectral Sequence for a Locally Free Sheaf Cohomology of a Supermanifold

Vishnyakova

2012

Geometric Methods in Physics

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Superstring field theory, superforms and supergeometry

Catenacci

Grassi

Noja

2020

Journal of Geometry and Physics

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Inspired by superstring field theory, we study differential, integral, and inverse forms and their mutual relations on a supermanifold from a sheaf-theoretical point of view. In particular, the formal distributional properties of integral forms are recovered in this scenario in a geometrical way. Further, we show how inverse forms "extend" the ordinary de Rham complex on a supermanifold, thus providing a mathematical foundation of the Large Hilbert Space used in superstrings. Last, we briefly discuss how the Hodge diamond of a supermanifold looks like, and we explicitly compute it for super Riemann surfaces.

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