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Plurigenera of 3-folds and weighted hypersurfaces
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Fletcher,, Anthony Robert (1988) Plurigenera of 3-folds and weighted hypersurfaces. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1456659~S1
Abstract
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 > (⅟160)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.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Geometry, Algebraic, Singularities (Mathematics). | ||||
Official Date: | August 1988 | ||||
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Publication Status: | Unpublished | ||||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.) | ||||
Sponsors: | Science and Engineering Research Council (Great Britain) | ||||
Extent: | 107 leaves | ||||
Language: | eng |
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