# Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. III

@article{Nikulin2015DegenerationsOK, title={Degenerations of K{\"a}hlerian K3 surfaces with finite symplectic automorphism groups. III}, author={Viacheslav V. Nikulin}, journal={Izvestiya: Mathematics}, year={2015}, volume={81}, pages={985 - 1029} }

Following our papers [1] and [2] (Parts I and II), we classify degenerations of codimension 2 or more of Kählerian surfaces with finite symplectic automorphism groups. In [1] and [2] this was done for codimension .

## 6 Citations

### Classification of degenerations and Picard lattices of Kählerian K3 surfaces with symplectic automorphism group

- MathematicsIzvestiya: Mathematics
- 2019

In [1]–[6] we classified the degenerations and Picard lattices of Kählerian K3 surfaces with finite symplectic automorphism groups of high order. This classification was not considered for the…

### Classification of Picard lattices of K3 surfaces

- MathematicsIzvestiya: Mathematics
- 2018

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…

### Plane rational quartics and K3 surfaces

- Mathematics
- 2016

AbstractWe study actions of the symmetric group S4 on K3 surfaces X that satisfy the following condition: there exists an equivariant birational contraction $$\bar r:X \to \bar X$$r¯:X→X¯
to a K3…

### Umbral Moonshine and K3 Surfaces

- Mathematics
- 2014

Recently, 23 cases of umbral moonshine, relating mock modular forms and finite groups, have been discovered in the context of the 23 even unimodular Niemeier lattices. One of the 23 cases in fact…

### Communications in Mathematical Physics Umbral Moonshine and K 3 Surfaces

- Mathematics
- 2015

Recently, 23 cases of umbral moonshine, relating mock modular forms and finite groups, have been discovered in the context of the 23 even unimodular Niemeier lattices. One of the 23 cases in fact…

### Niemeier Lattices in the Free Fermionic Heterotic–String Formulation

- Physics
- 2017

The spinor–vector duality was discovered in free fermionic constructions of the heterotic string in four dimensions. It played a key role in the construction of heterotic–string models with an…

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Using the results of [1]–[3] on Kählerian K3 surfaces and Niemeier lattices, we classify degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups with emphasis on…

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We prove the main conjecture (Conjecture 7.1) of the paper [1]. Using this result, we classify degenerations of codimension 1 of Kählerian K3 surfaces with finite symplectic automorphism groups.

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