Smooth Complete Intersections with Positive-Definite Intersection Form

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 corresp...

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Main Author:	Smirnov, ILIA
Other Authors:	Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))
Language:	en en_US
Published:	2012
Subjects:	Algebraic Geometry Mathematics
Online Access:	http://hdl.handle.net/1974/7602

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spelling	ndltd-LACETR-oai-collectionscanada.gc.ca-OKQ.1974-76022013-12-20T03:40:54ZSmooth Complete Intersections with Positive-Definite Intersection FormSmirnov, ILIAAlgebraic GeometryMathematicsWe 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 13:19:42.654Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))2012-10-15 13:19:42.6542012-10-16T15:20:14Z2012-10-16T15:20:14Z2012-10-16Thesishttp://hdl.handle.net/1974/7602enen_USCanadian thesesThis 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.
collection	NDLTD
language	en en_US
sources	NDLTD
topic	Algebraic Geometry Mathematics
spellingShingle	Algebraic Geometry Mathematics Smirnov, ILIA Smooth Complete Intersections with Positive-Definite Intersection Form
description	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
author2	Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))
author_facet	Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.)) Smirnov, ILIA
author	Smirnov, ILIA
author_sort	Smirnov, ILIA
title	Smooth Complete Intersections with Positive-Definite Intersection Form
title_short	Smooth Complete Intersections with Positive-Definite Intersection Form
title_full	Smooth Complete Intersections with Positive-Definite Intersection Form
title_fullStr	Smooth Complete Intersections with Positive-Definite Intersection Form
title_full_unstemmed	Smooth Complete Intersections with Positive-Definite Intersection Form
title_sort	smooth complete intersections with positive-definite intersection form
publishDate	2012
url	http://hdl.handle.net/1974/7602
work_keys_str_mv	AT smirnovilia smoothcompleteintersectionswithpositivedefiniteintersectionform
_version_	1716621504805863424

Smooth Complete Intersections with Positive-Definite Intersection Form

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