On the symplectic eightfold associated to a Pfaffian cubic fourfold
- Publication type:
- Journal article
- Metadata:
-
- Autoren
- Nicolas Addington
- Manfred Lehn
- Autoren-URL
- https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=fis-test-1&SrcAuth=WosAPI&KeyUT=WOS:000412119500004&DestLinkType=FullRecord&DestApp=WOS_CPL
- DOI
- 10.1515/crelle-2014-0145
- eISSN
- 1435-5345
- Externe Identifier
- Clarivate Analytics Document Solution ID: FI6PV
- ISSN
- 0075-4102
- Zeitschrift
- JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
- Paginierung
- 129 - 137
- Datum der Veröffentlichung
- 2017
- Status
- Published
- Titel
- On the symplectic eightfold associated to a Pfaffian cubic fourfold
- Sub types
- Article
- Ausgabe der Zeitschrift
- 731
Data source: Web of Science (Lite)
- Other metadata sources:
-
- Abstract
- <jats:title>Abstract</jats:title> <jats:p>We show that the irreducible holomorphic symplectic eightfold <jats:italic>Z</jats:italic> associated to a cubic fourfold <jats:italic>Y</jats:italic> not containing a plane is deformation-equivalent to the Hilbert scheme of four points on a K3 surface. We do this by constructing for a generic Pfaffian cubic <jats:italic>Y</jats:italic> a birational map <jats:inline-formula id="j_crelle-2014-0145_ineq_9999_w2aab3b7b3b1b6b1aab1c16b1b7Aa"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>Z</m:mi> <m:mo>→</m:mo> <m:mrow> <m:msup> <m:mi>Hilb</m:mi> <m:mn>4</m:mn> </m:msup> <m:mo></m:mo> <m:mrow> <m:mo>(</m:mo> <m:mi>X</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2014-0145_eq_mi119.png" /> <jats:tex-math>Z\to\operatorname{Hilb}^{4}(X)</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:italic>X</jats:italic> is the K3 surface associated to <jats:italic>Y</jats:italic> by Beauville and Donagi. We interpret <jats:italic>Z</jats:italic> as a moduli space of complexes on <jats:italic>X</jats:italic> and observe that at some point of <jats:italic>Z</jats:italic>, hence on a Zariski open subset, the complex is just the ideal sheaf of four points. This note is an appendix to <jats:ext-link ext-link-type="uri">http://dx.doi.org/10.1515/crelle-2014-0144</jats:ext-link>.</jats:p>
- Autoren
- Nicolas Addington
- Manfred Lehn
- DOI
- 10.1515/crelle-2014-0145
- eISSN
- 1435-5345
- ISSN
- 0075-4102
- Ausgabe der Veröffentlichung
- 731
- Zeitschrift
- Journal für die reine und angewandte Mathematik (Crelles Journal)
- Sprache
- en
- Online publication date
- 2015
- Paginierung
- 129 - 137
- Datum der Veröffentlichung
- 2017
- Status
- Published
- Herausgeber
- Walter de Gruyter GmbH
- Herausgeber URL
- http://dx.doi.org/10.1515/crelle-2014-0145
- Datum der Datenerfassung
- 2023
- Titel
- On the symplectic eightfold associated to a Pfaffian cubic fourfold
- Ausgabe der Zeitschrift
- 2017
Data source: Crossref
- Abstract
- We show that the irreducible holomorphic symplectic eightfold Z associated to a cubic fourfold Y not containing a plane is deformation-equivalent to the Hilbert scheme of four points on a K3 surface. We do this by constructing for a generic Pfaffian cubic Y a birational map Z ---> Hilb^4(X), where X is the K3 surface associated to Y by Beauville and Donagi. We interpret Z as a moduli space of complexes on X and observe that at some point of Z, hence on a Zariski open subset, the complex is just the ideal sheaf of four points.
- Autoren
- N Addington
- M Lehn
- Autoren-URL
- http://arxiv.org/abs/1404.5657v2
- Zeitschrift
- J. reine angew. Math.
- Schlüsselwörter
- math.AG
- math.AG
- Notes
- 9 pages. Minor changes; to appear in Crelle as an appendix to 1305.0178
- Paginierung
- 129 - 137
- Datum der Veröffentlichung
- 2014
- Herausgeber URL
- http://dx.doi.org/10.1515/crelle-2014-0145
- Datum der Datenerfassung
- 2014
- Datum, an dem der Datensatz öffentlich gemacht wurde
- 2014
- Titel
- On the symplectic eightfold associated to a Pfaffian cubic fourfold
- Ausgabe der Zeitschrift
- 731
Files
1404.5657v2.pdf
Data source: arXiv
- Autoren
- Nicolas Addington
- Manfred Lehn
- DOI
- 10.1515/crelle-2014-0145
- ISSN
- 0075-4102
- Zeitschrift
- Journal für die Reine und Angewandte Mathematik. [Crelle’s Journal]
- Notes
- mrclass: 14C05 (14D15 14F05 14J28) mrnumber: 3709062 mrreviewer: Kieran G. O’Grady
- Paginierung
- 129 - 137
- Datum der Veröffentlichung
- 2017
- Herausgeber URL
- https://doi.org/10.1515/crelle-2014-0145
- Datum der Datenerfassung
- 2019
- Titel
- On the symplectic eightfold associated to a Pfaffian cubic fourfold
- Sub types
- article
- Ausgabe der Zeitschrift
- 731
Data source: Manual
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