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Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 5, Pages 109–154 (Mi izv8016)  

This article is cited in 10 scientific papers (total in 10 papers)

Kählerian K3 surfaces and Niemeier lattices. I

V. V. Nikulinab

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

Abstract: Using the results obtained in [1], Remark 1.14.7, we clarify the relation between Kählerian $\mathrm{K3}$ surfaces and Niemeier lattices. We emphasize that all 24 Niemeier lattices are important in the description of $\mathrm{K3}$ surfaces, not only the one related to the Mathieu group.

Keywords: $\mathrm{K3}$ surface, Kählerian surface, automorphism group, integer quadratic form.

DOI: https://doi.org/10.4213/im8016

Full text: PDF file (804 kB)
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English version:
Izvestiya: Mathematics, 2013, 77:5, 954–997

Bibliographic databases:

Document Type: Article
UDC: 512.774.4+512.774.2+512.542+512.647.2
PACS: 02.10.De, 02.40.Tt
MSC: 14J28, 11H56
Received: 25.06.2012
Revised: 26.11.2012

Citation: V. V. Nikulin, “Kählerian K3 surfaces and Niemeier lattices. I”, Izv. RAN. Ser. Mat., 77:5 (2013), 109–154; Izv. Math., 77:5 (2013), 954–997

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. C. N. Cheng, S. Harrison, “Umbral moonshine and $K3$ surfaces”, Comm. Math. Phys., 339:1 (2015), 221–261  crossref  mathscinet  zmath  isi  scopus
    2. V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups”, Izv. Math., 79:4 (2015), 740–794  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. II”, Izv. Math., 80:2 (2016), 359–402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. V. V. Nikulin, “Kählerian K3 Surfaces and Niemeier Lattices, II”, Development of moduli theory—Kyoto 2013, Adv. Stud. Pure Math., 69, eds. Fujino O., Kondo S., Moriwaki A., Saito M., Yoshioka K., Math. Soc. Japan, Tokyo, 2016, 421–471  mathnet  mathscinet  zmath  isi
    5. M. C. N. Cheng, F. Ferrari, S. M. Harrison, N. M. Paquette, “Landau-Ginzburg orbifolds and symmetries of K$_3$ CFTs”, J. High Energy Phys., 2017, no. 1, 046, front matter+48 pp.  crossref  mathscinet  isi  scopus
    6. V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. III”, Izv. Math., 81:5 (2017), 985–1029  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. Sh. Kachru, N. M. Paquette, R. Volpato, “3D string theory and umbral moonshine”, J. Phys. A, 50:40 (2017), 404003, 21 pp.  crossref  mathscinet  zmath  isi  scopus
    8. N. M. Paquette, R. Volpato, M. Zimet, “No more walls! A tale of modularity, symmetry, and wall crossing for 1/4 BPS dyons”, J. High Energy Phys., 2017, no. 5, 047, front matter+76 pp.  crossref  mathscinet  isi  scopus
    9. Cheng M.C.N. Harrison S.M. Volpato R. Zimet M., “K3 String Theory, Lattices and Moonshine”, Res. Math. Sci., 5 (2018), 32  crossref  mathscinet  zmath  isi
    10. V. V. Nikulin, “Classification of Picard lattices of K3 surfaces”, Izv. Math., 82:4 (2018), 752–816  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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