We classify the smooth complete intersections with positive-definite intersection form on their middle cohomology. There are two families. The first family are quadric hypersurfaces in P(4k+1) with k a positive integer. The middle cohomology is always of rank two and the intersection lattice corresponds to the identity matrix. The second family are complete intersections of two quadrics in P(4k+2) (k a positive integer). Here the intersection lattices are the Gamma(4(k+1)) lattices; in particular, the intersection lattice of a smooth complete intersection of two quadrics in P(6) is the famous E8 lattice. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2012-10-15 13:19:42.654
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OKQ.1974/7602 |
| Date | 16 October 2012 |
| Creators | Smirnov, ILIA |
| Contributors | Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.)) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English, en_US |
| Detected Language | English |
| Type | Thesis |
| Rights | This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner. |
| Relation | Canadian theses |
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