Automorphisms of finite order on Gorenstein del Pezzo surfaces

Author:
D.-Q. Zhang

Journal:
Trans. Amer. Math. Soc. **354** (2002), 4831-4845

MSC (2000):
Primary 14J50; Secondary 14J26

Published electronically:
August 1, 2002

MathSciNet review:
1926853

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Abstract: In this paper we shall determine all actions of groups of prime order with on Gorenstein del Pezzo (singular) surfaces of Picard number 1. We show that every order- element in ( , being the minimal resolution of ) is lifted from a projective transformation of . We also determine when is finite in terms of , and the number of singular members in . In particular, we show that either for some , or for every prime , there is at least one element of order in (hence is infinite).

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Additional Information

**D.-Q. Zhang**

Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore

Email:
matzdq@math.nus.edu.sg

DOI:
http://dx.doi.org/10.1090/S0002-9947-02-03069-6

Received by editor(s):
March 10, 2002

Published electronically:
August 1, 2002

Article copyright:
© Copyright 2002
American Mathematical Society