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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 1, Pages 99–122 (Mi izv1143)  

This article is cited in 6 scientific papers (total in 6 papers)

On the connected components of moduli of real polarized K3-surfaces

V. V. Nikulinab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Department of Mathematical Sciences, University of Liverpool

Abstract: We complete the investigations in [11] on the classification of connected components of moduli of real polarized K3-surfaces. In particular, we show that this classification is closely related to some classical problems in number theory: the classification of binary indefinite lattices and the representation of integers as sums of two squares. As an application, we use recent results in [13] to completely classify real polarized K3-surfaces that are deformations of real hyperelliptically polarized K3-surfaces. This is important because real hyperelliptically polarized K3-surfaces can be constructed explicitly.

Keywords: deformation, real $K3$ surface, moduli, connected component, hyperelliptic curve, linear system, real rational surface, ellipsoid, hyperboloid, polarization

DOI: https://doi.org/10.4213/im1143

Full text: PDF file (599 kB)
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English version:
Izvestiya: Mathematics, 2008, 72:1, 91–111

Bibliographic databases:

Document Type: Article
UDC: 512.774.5+511.334
MSC: 14H45, 14J26, 14J28, 14P25
Received: 12.07.2006

Citation: V. V. Nikulin, “On the connected components of moduli of real polarized K3-surfaces”, Izv. RAN. Ser. Mat., 72:1 (2008), 99–122; Izv. Math., 72:1 (2008), 91–111

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Finashin S., Kharlamov V., “On the deformation chirality of real cubic fourfolds”, Compos. Math., 145:5 (2009), 1277–1304  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. A. Krasnov, “Maximal intersections of three real quadrics”, Izv. Math., 75:3 (2011), 569–587  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. V. A. Krasnov, “Real Two-Dimensional Intersections of a Quadric by a Cubic”, Math. Notes, 90:4 (2011), 509–516  mathnet  crossref  crossref  mathscinet  isi
    4. V. A. Krasnov, “Real $M$-triquadrics”, Izv. Math., 77:1 (2013), 30–43  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. V. A. Krasnov, “On a classical correspondence of real K3 surfaces”, Izv. Math., 82:4 (2018), 662–693  mathnet  crossref  crossref  adsnasa  isi  elib
    6. V. A. Krasnov, “Real Kummer surfaces”, Izv. Math., 83:1 (2019), 65–103  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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