Translator Disclaimer
15 March 2004 Finiteness and quasi-simplicity for symmetric K3 -surfaces
Alex Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov
Duke Math. J. 122(1): 1-49 (15 March 2004). DOI: 10.1215/S0012-7094-04-12211-8

Abstract

We compare the smooth and deformation equivalence of actions of finite groups on K3 -surfaces by holomorphic and antiholomorphic transformations. We prove that the number of deformation classes is finite and, in a number of cases, establish the expected coincidence of the two equivalence relations. More precisely, in these cases we show that an action is determined by the induced action in the homology. On the other hand, we construct two examples to show first that, in general, the homological type of an action does not even determine its topological type, and second that K3 -surfaces X and X ¯ with the same Klein action do not need to be equivariantly deformation equivalent even if the induced action on H 2,0 (X) is real, that is, reduces to multiplication by ±1 .

Citation

Download Citation

Alex Degtyarev. Ilia Itenberg. Viatcheslav Kharlamov. "Finiteness and quasi-simplicity for symmetric K3 -surfaces." Duke Math. J. 122 (1) 1 - 49, 15 March 2004. https://doi.org/10.1215/S0012-7094-04-12211-8

Information

Published: 15 March 2004
First available in Project Euclid: 24 March 2004

zbMATH: 1073.14053
MathSciNet: MR2046806
Digital Object Identifier: 10.1215/S0012-7094-04-12211-8

Subjects:
Primary: 14J28, 14J50
Secondary: 14P25, 32G05, 57S17

Rights: Copyright © 2004 Duke University Press

JOURNAL ARTICLE
49 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.122 • No. 1 • 15 March 2004
Back to Top