Moduli of Double EPW-Sextics. (Record no. 127891)
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| fixed length control field | 05833nam a22005053i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC4901855 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729131324.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2016 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470428242 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470416966 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC4901855 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL4901855 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)938499830 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA573 .O47 2015 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.3/53 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Oâe(tm)Grady, Kieran G. |
| 245 10 - TITLE STATEMENT | |
| Title | Moduli of Double EPW-Sextics. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2016. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2015. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (188 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.240 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 0. Introduction -- Chapter 1. Preliminaries -- 1.1. EPW-sextics and their double covers -- 1.2. Double EPW-sextics modulo isomorphisms -- 1.3. The GIT quotient -- 1.4. Moduli of plane sextics -- Chapter 2. One-parameter subgroups and stability -- 2.1. Outline of the section -- 2.2. (Semi)stability and flags -- 2.3. The Cone Decomposition Algorithm -- 2.4. The standard non-stable strata -- 2.4.1. The definitions -- 2.4.2. Geometric significance of certain strata -- 2.5. The stable locus -- 2.6. The GIT-boundary -- Chapter 3. Plane sextics and stability of lagrangians -- 3.1. The main result of the chapter -- 3.2. Plane sextics -- 3.3. Non-stable strata and plane sextics, I -- 3.4. Non-stable strata and plane sextics, II -- Chapter 4. Lagrangians with large stabilizers -- 4.1. Main results -- 4.2. A result of Luna -- 4.3. Lagrangians stabilized by a maximal torus -- 4.4. Lagrangians stabilized by \PGL(4) or \PSO(4) -- 4.5. Lagrangians stabilized by \PGL(3) -- Chapter 5. Description of the GIT-boundary -- 5.1. Main results -- 5.2. A GIT set-up for each standard non-stable stratum -- 5.2.1. Set-up -- 5.2.2. The Hilbert-Mumford numerical function -- 5.3. Summary of results of Chapters 6 and 7 -- 5.4. Proof of Theorem 5.1.1 assuming the results of Chapters 6 and 7 -- 5.4.1. Dimensions -- 5.4.2. No inclusion relations -- Chapter 6. Boundary components meeting ℑ in a subset of _{ }∪{ , ^{∨}} -- 6.1. \gB_{\cC₁} -- 6.1.1. First results -- 6.1.2. Properly semistable points of ^{\sF}_{\cC₁} -- 6.1.3. Semistable lagrangians with dimΘ_{ }≥2 or _{ , }=\PP( ). -- 6.1.4. Analysis of Θ_{ } and _{ , } -- 6.1.5. Wrapping it up -- 6.2. \gB_{\cA} -- 6.2.1. The GIT analysis -- 6.2.2. Analysis of Θ_{ } and _{ , } -- 6.2.3. Wrapping it up -- 6.3. \gB_{\cD} -- 6.3.1. Quadrics associated to ∈ ^{\sF}_{\cD} -- 6.3.2. The GIT analysis. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 6.3.3. Analysis of Θ_{ } and _{ , } -- 6.3.4. Wrapping it up -- 6.4. \gB_{\cE₁} -- 6.4.1. The GIT analysis -- 6.4.2. Analysis of Θ_{ } and _{ , } -- 6.4.3. Wrapping it up -- 6.5. \gB_{\cE^{∨}₁} -- 6.5.1. The GIT analysis -- 6.5.2. Analysis of Θ_{ } and _{ , } -- 6.5.3. Wrapping it up -- 6.6. \gB_{\cF₁} -- 6.6.1. The GIT analysis -- 6.6.2. Analysis of Θ_{ } and _{ , } -- 6.6.3. Wrapping it up -- Chapter 7. The remaining boundary components -- 7.1. \gB_{\cF₂} -- 7.2. \gB_{\cF₂}∩\gI -- 7.2.1. Set-up and statement of the main results -- 7.2.2. The 3-fold swept out by the projective planes parametrized by ₊( ) -- 7.2.3. Explicit description of \WW^{ }_{ }. -- 7.2.4. \gX_{\cV} is irreducible of dimension 3 -- 7.2.5. Points of \gB_{\cF₂}∩\gI are represented by lagrangians in \WW^{ }_{ } -- 7.2.6. _{ , } for ∈\XX^{ }_{\cV} and spanned by ∈ ₀₁, ∈ ₂₃ and ∈ ₄₅ -- 7.2.7. Proof that \gB_{\cF₂}∩\gI=\gX_{\cV} -- 7.3. \gX_{\cN₃} -- 7.4. \gX_{\cN₃}∩\gI -- 7.4.1. Set-up and statement of the main results -- 7.4.2. Duality -- 7.4.3. Properties of \gX_{\cZ} -- 7.4.4. Points of \gX_{\cN₃}∩\gI are represented by lagrangians in \YY^{ }_{ } -- 7.4.5. Proof that \gX_{\cN₃}∩\gI=\gX_{\cW}∪\gX_{\cZ} -- Appendix A. Elementary auxiliary results -- A.1. Discriminant of quadratic forms -- A.2. Quadratic forms of corank 2 -- A.3. Pencils of degenerate linear maps -- Appendix B. Tables -- Bibliography -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of \bigwedge^3{\mathbb C}^6 modulo the natural action of \mathrm{SL}_6, call it \mathfrak{M}. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK 4-folds of Type K3^{[2]} polarized by a divisor of square 2 for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic 4-folds. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Surfaces, Sextic. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Equations, Sextic. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Permutation groups. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Hypersurfaces. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Geometry, Algebraic. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Oâe(tm)Grady, Kieran G. |
| Title | Moduli of Double EPW-Sextics |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2016 |
| International Standard Book Number | 9781470416966 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901855">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901855</a> |
| Public note | Click to View |
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