Title	Large Lefschetz defects
Creator	Cook II, David
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2016-03-15T10:31
Description	Mezzetti, Mir´o-Roig, and Ottaviani showed that in some cases the failure of the weak Lefschetz property can be used to produce a variety satisfying a Laplace equation. We define a graded algebra to have a Lefschetz defect of ! in degree d if the rank of the multiplication map of a general linear form between the degree d−1 and degree d components has rank ! less than the expected rank. Mezzetti and Mir´o-Roig recently explored the minimal and maximal number of generators of ideals that fail to have the weak Lefschetz property, i.e., to have a positive Lefschetz defect. In contrast to this, we will discuss constructions of ideals that have large Lefschetz defects and thus can be used to produce toric varieties satisfying many Laplace equations.
Extent	30 minutes
Subject	Mathematics; Commutative rings and algebras; Several complex variables and analytic spaces; Commutative algebra
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Eastern Illinois University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2016-09-20
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0314357
URI	http://hdl.handle.net/2429/59225
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Large Lefschetz defects Cook II, David

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