Classifying affine line bundles on a compact complex space

The classification of affine line bundles on a compact complex space is a difficult problem. We study the affine analogue of the Picard functor and the representability problem for this functor. Let be a compact complex space with . We introduce the affine Picard functor which assigns to a complex...

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Autor principal:	Plechinger Valentin
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2019
Materias:	representable functor affine bundle 32g13 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e80dfb7252a24bf9bd14208815264b37
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spelling	oai:doaj.org-article:e80dfb7252a24bf9bd14208815264b372021-12-02T19:08:48ZClassifying affine line bundles on a compact complex space2300-744310.1515/coma-2019-0005https://doaj.org/article/e80dfb7252a24bf9bd14208815264b372019-02-01T00:00:00Zhttps://doi.org/10.1515/coma-2019-0005https://doaj.org/toc/2300-7443The classification of affine line bundles on a compact complex space is a difficult problem. We study the affine analogue of the Picard functor and the representability problem for this functor. Let be a compact complex space with . We introduce the affine Picard functor which assigns to a complex space the set of families of linearly -framed affine line bundles on parameterized by . Our main result states that the functor is representable if and only if the map is constant. If this is the case, the space which represents this functor is a linear space over whose underlying set is , where is a Poincaré line bundle normalized at . The main idea idea of the proof is to compare the representability of to the representability of a functor considered by Bingener related to the deformation theory of -cohomology classes. Our arguments show in particular that, for = 1, the converse of Bingener’s representability criterion holdsPlechinger ValentinDe Gruyterarticlerepresentable functoraffine bundle32g13MathematicsQA1-939ENComplex Manifolds, Vol 6, Iss 1, Pp 103-117 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	representable functor affine bundle 32g13 Mathematics QA1-939
spellingShingle	representable functor affine bundle 32g13 Mathematics QA1-939 Plechinger Valentin Classifying affine line bundles on a compact complex space
description	The classification of affine line bundles on a compact complex space is a difficult problem. We study the affine analogue of the Picard functor and the representability problem for this functor. Let be a compact complex space with . We introduce the affine Picard functor which assigns to a complex space the set of families of linearly -framed affine line bundles on parameterized by . Our main result states that the functor is representable if and only if the map is constant. If this is the case, the space which represents this functor is a linear space over whose underlying set is , where is a Poincaré line bundle normalized at . The main idea idea of the proof is to compare the representability of to the representability of a functor considered by Bingener related to the deformation theory of -cohomology classes. Our arguments show in particular that, for = 1, the converse of Bingener’s representability criterion holds
format	article
author	Plechinger Valentin
author_facet	Plechinger Valentin
author_sort	Plechinger Valentin
title	Classifying affine line bundles on a compact complex space
title_short	Classifying affine line bundles on a compact complex space
title_full	Classifying affine line bundles on a compact complex space
title_fullStr	Classifying affine line bundles on a compact complex space
title_full_unstemmed	Classifying affine line bundles on a compact complex space
title_sort	classifying affine line bundles on a compact complex space
publisher	De Gruyter
publishDate	2019
url	https://doaj.org/article/e80dfb7252a24bf9bd14208815264b37
work_keys_str_mv	AT plechingervalentin classifyingaffinelinebundlesonacompactcomplexspace
_version_	1718377183156633600

Classifying affine line bundles on a compact complex space

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