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Deligne pairings and discriminants of algebraic varieties
Descriptive
TitleInfo
Title
Deligne pairings and discriminants of algebraic varieties
Name
(type = personal)
NamePart
(type = family)
Kapadia
NamePart
(type = given)
Hetal Manilal
NamePart
(type = date)
1983-
DisplayForm
Hetal Kapadia
Role
RoleTerm
(authority = RULIB)
author
Name
(type = personal)
NamePart
(type = family)
Sturm
NamePart
(type = given)
Jacob
DisplayForm
Jacob Sturm
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
chair
Name
(type = personal)
NamePart
(type = family)
Loftin
NamePart
(type = given)
John
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John Loftin
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Wang
NamePart
(type = given)
Xiaowei
DisplayForm
Xiaowei Wang
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
McFeron
NamePart
(type = given)
Donovan
DisplayForm
Donovan McFeron
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
outside member
Name
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NamePart
Rutgers University
Role
RoleTerm
(authority = RULIB)
degree grantor
Name
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NamePart
Graduate School - Newark
Role
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school
TypeOfResource
Text
Genre
(authority = marcgt)
theses
OriginInfo
DateCreated
(qualifier = exact)
2014
DateOther
(qualifier = exact);
(type = degree)
2014-05
Place
PlaceTerm
(type = code)
xx
Language
LanguageTerm
(authority = ISO639-2b);
(type = code)
eng
Abstract
(type = abstract)
Let V be a finite dimensional complex vector space, V^∗ its dual, and let X ⊂ P(V ) be a smooth projective variety of dimension n and degree d ≥ 2. For a generic n−tuple of hyperplanes (H_1, ..., H_n) ∈ P(V^∗)^n, the intersection X ∩ H_1 ∩ · · · ∩ H_n consists of d distinct points. We define the “discriminant of X” to be the set D_X of n-tuples for which the set-theoretic intersection is not equal to d points. Then D_X ⊂ P(V^∗)^n is a hypersurface and the set of defining polynomials, which is a one-dimensional vector space, is called the “discriminant line”. We show that this line is canonically isomorphic to the Deligne pairing ⟨KL^n,...,L⟩ where K is the canonical line bundle of X and L → X is the restriction of the hyperplane bundle. As a corollary, we obtain a generalization of Paul’s formula [14] which relates the Mabuchi K-energy on the space of Bergman metrics to ∆X, the “hyperdiscriminant of X”.
Subject
(authority = RUETD)
Topic
Mathematical Sciences
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
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ETD
Identifier
ETD_5592
PhysicalDescription
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electronic resource
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application/pdf
InternetMediaType
text/xml
Extent
v, 34 p. : ill.
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = vita)
Includes vita
Note
(type = statement of responsibility)
by Hetal Manilal Kapadia
Subject
(authority = ETD-LCSH)
Topic
Vector analysis
Subject
(authority = ETD-LCSH)
Topic
Algebra, Universal
RelatedItem
(type = host)
TitleInfo
Title
Graduate School - Newark Electronic Theses and Dissertations
Identifier
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rucore10002600001
Location
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(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T34Q7S8B
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
RightsDeclaration
(ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder
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Name
FamilyName
Kapadia
GivenName
Hetal
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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(qualifier = exact);
(point = start)
2014-04-28 13:39:59
AssociatedEntity
Name
Hetal Kapadia
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - Newark
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical
RULTechMD
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ContentModel
ETD
OperatingSystem
(VERSION = 5.1)
windows xp
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