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Title: Plurigenera of 3-folds and weighted hypersurfaces
Author: Fletcher, Anthony Robert
ISNI:       0000 0001 3469 2891
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1988
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Chapter I gives basic results and definitions for nonsingular varieties, normal varieties and canonical singularities. In Chapter II we give alternative forms of the Riemann-Roch formula for projec­tive 3-folds with at worst canonical singularities. We show for a canonical 3-fold X with x(Ox) « 1 that Pl2(X) > 1. Pu(X) > 2 and K3x > (1⁄160)3. The last section of Chapter II shows that the record of pluridata representing a canonical 3-fold is unique. In Chapter III we find necessary and sufficient conditions for weighted complete intersections of codimensions 1 and 2 to be quasismooth. We also give conditions for quasismooth surface and 3-fold intersections of codimension 1 and 2 to have at worst only isolated canonical singularities. We produce lists of such complete inter­sections in two different ways: one using these conditions for quasismoothness and having only isolated canonical singularities and the second deducing the degrees of the generators and relations from the plurigenera via the Poincaré series of the canonical ring.
Supervisor: Not available Sponsor: Science and Engineering Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics