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Quasiprojectivity of images of mixed period maps

dc.contributor.authorBAKKER, Benjamin
hal.structure.identifierCentre National de la Recherche Scientifique [CNRS]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBRUNEBARBE, Yohan
dc.contributor.authorTSIMERMAN, Jacob
dc.date.accessioned2024-04-04T02:48:21Z
dc.date.available2024-04-04T02:48:21Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191731
dc.description.abstractEnWe prove a mixed version of a conjecture of Griffiths: that the closure of the image of any admissible mixed period map is quasiprojective, with a natural ample bundle. Specifically, we consider the map from the image of the mixed period map to the image of the period map of the associated graded. On the one hand, we show in a precise manner that the parts of this map parametrizing extension data of non-adjacent-weight pure Hodge structures are quasi-affine. On the other hand, extensions of adjacent-weight pure polarized Hodge structures are parametrized by a compact complex torus (the intermediate Jacobian) equipped with a natural theta bundle which is ample in Griffiths transverse directions. Our proof makes heavy use of o-minimality, and recent work with B. Klingler associating a $\mathbb{R}_{an,exp}$-definable structure to mixed period domains and admissible mixed period maps.
dc.language.isoen
dc.title.enQuasiprojectivity of images of mixed period maps
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]
dc.identifier.arxiv2006.13709
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-03064621
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03064621v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BAKKER,%20Benjamin&BRUNEBARBE,%20Yohan&TSIMERMAN,%20Jacob&rft.genre=preprint


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