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Duality of families of K3 surfaces and bimodal singularities Mase, Makiko
Description
As a generalisation of Arnold's strange duality for unimodal singularities, Ebeling and Takahashi introduced a notion of strange duality for invertible polynomials, which shows a mirror symmetric phenomenon. For each of bimodal singularities, Ebeling produced a Coxeter-Dynkin diagram with respect to a distinguished basis of vanishing cycles by means of its defining equation, which is understood geometrically by Ebeling and Ploog. In my talk, we consider strange-dual pairs of bimodal singularities together with the projectivisations obtained by the one in Ebeling and Ploog's work, by which, we can construct families of K3 surfaces. We discuss whether or not the strange duality extends to dualities of polytopes and lattices for the families. As a consequence, we present that every strange-dual pair can extend to polytope duality, whilst with some exceptions, can extend to lattice duality, and a Hodge-theoretical reason for the lattice duality not being held.
Item Metadata
Title |
Duality of families of K3 surfaces and bimodal singularities
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-11-01T11:06
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Description |
As a generalisation of Arnold's strange duality for unimodal singularities, Ebeling and Takahashi introduced a notion of strange duality for invertible polynomials, which shows a mirror symmetric phenomenon. For each of bimodal singularities, Ebeling produced a Coxeter-Dynkin diagram with respect to a distinguished basis of vanishing cycles by means of its defining equation, which is understood geometrically by Ebeling and Ploog.
In my talk, we consider strange-dual pairs of bimodal singularities together with the projectivisations obtained by the one in Ebeling and Ploog's work, by which, we can construct families of K3 surfaces. We discuss whether or not the strange duality extends to dualities of polytopes and lattices for the families.
As a consequence, we present that every strange-dual pair can extend to polytope duality, whilst with some exceptions, can extend to lattice duality, and a Hodge-theoretical reason for the lattice duality not being held.
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Extent |
42.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Tokyo Metropolitan University
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Series | |
Date Available |
2019-05-01
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0378532
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Researcher
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International