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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 4, Pages 115–177 (Mi izv8719)  

Classification of Picard lattices of K3 surfaces

V. V. Nikulinab

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

Abstract: Using the results of our papers [1]–[4] on the classification of degenerations of Kählerian K3 surfaces, we classify the Picard lattices of Kählerian K3 surfaces. By classification we mean classification depending on their possible finite symplectic automorphism groups and their non-singular rational curves when the Picard lattice is negative definite.

Keywords: K3 surface, complex surface, Picard lattice, automorphism group, rational curve, degeneration, integer symmetric bilinear form.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/im8719

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English version:
Izvestiya: Mathematics, 2018, 82:4, 752–816

Bibliographic databases:

Document Type: Article
UDC: 512.774.4+515.173.4+512.722+512.774.2+512.774.3+512.647.2
MSC: 14J28, 14J10, 14C22, 14J50
Received: 15.09.2017

Citation: V. V. Nikulin, “Classification of Picard lattices of K3 surfaces”, Izv. RAN. Ser. Mat., 82:4 (2018), 115–177; Izv. Math., 82:4 (2018), 752–816

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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