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Title: Hodge theory in Grassmannians
Author: Fatighenti, Enrico
ISNI:       0000 0004 7223 894X
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2017
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics