Twisted cubics on cubic fourfolds

Publication type:
Journal article
Metadata:
Autoren
  • Christian Lehn
  • Manfred Lehn
  • Christoph Sorger
  • Duco van Straten
Autoren-URL
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=fis-test-1&SrcAuth=WosAPI&KeyUT=WOS:000412119500003&DestLinkType=FullRecord&DestApp=WOS_CPL
DOI
10.1515/crelle-2014-0144
eISSN
1435-5345
Externe Identifier
  • Clarivate Analytics Document Solution ID: FI6PV
ISSN
0075-4102
Zeitschrift
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
Paginierung
87 - 128
Datum der Veröffentlichung
2017
Status
Published
Titel
Twisted cubics on cubic fourfolds
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 construct a new twenty-dimensional family of projective eight-dimensional irreducible holomorphic symplectic manifolds: the compactified moduli space <jats:inline-formula id="j_crelle-2014-0144_ineq_9999_w2aab3b7b2b1b6b1aab1c16b1b1Aa"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>M</m:mi> <m:mn>3</m:mn> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mi>Y</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2014-0144_eq_mi496.png" /> <jats:tex-math>M_{3}(Y)</jats:tex-math> </jats:alternatives> </jats:inline-formula> of twisted cubics on a smooth cubic fourfold <jats:italic>Y</jats:italic> that does not contain a plane is shown to be smooth and to admit a contraction <jats:inline-formula id="j_crelle-2014-0144_ineq_9998_w2aab3b7b2b1b6b1aab1c16b1b5Aa"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:msub> <m:mi>M</m:mi> <m:mn>3</m:mn> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mi>Y</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mo>→</m:mo> <m:mrow> <m:mi>Z</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mi>Y</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-2014-0144_eq_mi497.png" /> <jats:tex-math>M_{3}(Y)\to Z(Y)</jats:tex-math> </jats:alternatives> </jats:inline-formula> to a projective eight-dimensional symplectic manifold <jats:inline-formula id="j_crelle-2014-0144_ineq_9997_w2aab3b7b2b1b6b1aab1c16b1b7Aa"> <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:mo>(</m:mo> <m:mi>Y</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2014-0144_eq_mi624.png" /> <jats:tex-math>Z(Y)</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The construction is based on results on linear determinantal representations of singular cubic surfaces.</jats:p>
Autoren
  • Christian Lehn
  • Manfred Lehn
  • Christoph Sorger
  • Duco van Straten
DOI
10.1515/crelle-2014-0144
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
87 - 128
Datum der Veröffentlichung
2017
Status
Published
Herausgeber
Walter de Gruyter GmbH
Herausgeber URL
http://dx.doi.org/10.1515/crelle-2014-0144
Datum der Datenerfassung
2023
Titel
Twisted cubics on cubic fourfolds
Ausgabe der Zeitschrift
2017

Data source: Crossref

Abstract
We construct a new twenty-dimensional family of projective eight-dimensional irreducible holomorphic symplectic manifolds: the compactified moduli space M_3(Y) of twisted cubics on a smooth cubic fourfold Y that does not contain a plane is shown to be smooth and to admit a contraction M_3(Y) -> Z(Y) to a projective eight-dimensional symplectic manifold Z(Y). The construction is based on results on linear determinantal representations of singular cubic surfaces.
Autoren
  • Christian Lehn
  • Manfred Lehn
  • Christoph Sorger
  • Duco van Straten
Autoren-URL
http://arxiv.org/abs/1305.0178v2
Schlüsselwörter
  • math.AG
  • math.AG
  • Primary 14C05, 14C21, 14J10, Secondary 14J26, 14J35, 14J70
Notes
A proof that Z(Y) is simply-connected and irreducible hyperk\"ahler has been added. A couple of typos corrected
Datum der Veröffentlichung
2013
Datum der Datenerfassung
2013
Datum, an dem der Datensatz öffentlich gemacht wurde
2013
Titel
Twisted cubics on cubic fourfolds

Files

1305.0178v2.pdf

Data source: arXiv

Autoren
  • Christian Lehn
  • Manfred Lehn
  • Christoph Sorger
  • Duco van Straten
DOI
10.1515/crelle-2014-0144
ISSN
0075-4102
Zeitschrift
Journal für die Reine und Angewandte Mathematik. [Crelle’s Journal]
Notes
mrclass: 14C05 (14J28 14J35 53D30) mrnumber: 3709061 mrreviewer: Arnaud Beauville
Paginierung
87 - 128
Datum der Veröffentlichung
2017
Herausgeber URL
https://doi.org/10.1515/crelle-2014-0144
Datum der Datenerfassung
2019
Titel
Twisted cubics on cubic fourfolds
Sub types
  • article
Ausgabe der Zeitschrift
731

Data source: Manual

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