Moduli spaces of polarized irreducible symplectic manifolds are not necessarily connected

Apostol Apostolov[1]

  • [1] Leibniz Universitat Hannover Institute of Algebraic Geometry Gottfried Wilhelm Leibniz Universität Hannover Welfengarten 1 30167 Hannover (Allemagne)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 1, page 189-202
  • ISSN: 0373-0956

Abstract

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We show that the moduli space of polarized irreducible symplectic manifolds of K 3 [ n ] -type, of fixed polarization type, is not always connected. This can be derived as a consequence of Eyal Markman’s characterization of polarized parallel-transport operators of K 3 [ n ] -type.

How to cite

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Apostolov, Apostol. "Moduli spaces of polarized irreducible symplectic manifolds are not necessarily connected." Annales de l’institut Fourier 64.1 (2014): 189-202. <http://eudml.org/doc/275577>.

@article{Apostolov2014,
abstract = {We show that the moduli space of polarized irreducible symplectic manifolds of $K3^\{[n]\}$-type, of fixed polarization type, is not always connected. This can be derived as a consequence of Eyal Markman’s characterization of polarized parallel-transport operators of $K3^\{[n]\}$-type.},
affiliation = {Leibniz Universitat Hannover Institute of Algebraic Geometry Gottfried Wilhelm Leibniz Universität Hannover Welfengarten 1 30167 Hannover (Allemagne)},
author = {Apostolov, Apostol},
journal = {Annales de l’institut Fourier},
keywords = {number of connected components; monodromy invariant; irreducible symplectic manifolds},
language = {eng},
number = {1},
pages = {189-202},
publisher = {Association des Annales de l’institut Fourier},
title = {Moduli spaces of polarized irreducible symplectic manifolds are not necessarily connected},
url = {http://eudml.org/doc/275577},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Apostolov, Apostol
TI - Moduli spaces of polarized irreducible symplectic manifolds are not necessarily connected
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 1
SP - 189
EP - 202
AB - We show that the moduli space of polarized irreducible symplectic manifolds of $K3^{[n]}$-type, of fixed polarization type, is not always connected. This can be derived as a consequence of Eyal Markman’s characterization of polarized parallel-transport operators of $K3^{[n]}$-type.
LA - eng
KW - number of connected components; monodromy invariant; irreducible symplectic manifolds
UR - http://eudml.org/doc/275577
ER -

References

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  12. Kieran G. O’Grady, Desingularized moduli spaces of sheaves on a K 3 , J. Reine Angew. Math. 512 (1999), 49-117 Zbl0928.14029MR1703077
  13. Kieran G. O’Grady, A new six-dimensional irreducible symplectic variety, J. Algebraic Geom. 12 (2003), 435-505 Zbl1068.53058MR1966024
  14. Jean-Pierre Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier, Grenoble 6 (1955–1956), 1-42 Zbl0075.30401MR82175
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  16. Eckart Viehweg, Quasi-projective moduli for polarized manifolds, 30 (1995), Springer-Verlag, Berlin Zbl0844.14004MR1368632

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