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Hodge theory in Grassmannians
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Fatighenti, Enrico (2017) Hodge theory in Grassmannians. PhD thesis, University of Warwick.
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WRAP_Theses_Fatighenti_2017.pdf - Submitted Version - Requires a PDF viewer. Download (1419Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3141955~S15
Abstract
In this thesis we study several generalisations of the Griffiths’s residue technique. We first show how the deformation modules Ti of the affine cone over a smooth projective variety X contain the Hodge groups of X as homogeneous slices. We discuss several applications, mainly in the Birational Geometry of Q-Fano threefolds. We then investigate the case of subvarieties of the Grassmannian Gr(k, n). For an hypersurfaces (or a complete intersection) X in the Grassmannian Gr(k, n) we are able to explicitly construct a Griffiths ring that allows us to compute all the Hodge groups Hp,q(X). We then apply our techniques to construct new interesting varieties in the Grassmannians, such as surfaces of general type with low invariants and Fano manifolds of K3-type.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Geometry, Algebraic, Hodge theory, Grassmann manifolds, Torelli theorem | ||||
Official Date: | November 2017 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Reid, Miles (Miles A.) | ||||
Format of File: | |||||
Extent: | xvi, 169 leaves : illustrations | ||||
Language: | eng |
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