Automorphisms of finite order on Gorenstein del Pezzo surfaces
Author:
D.Q. Zhang
Journal:
Trans. Amer. Math. Soc. 354 (2002), 48314845
MSC (2000):
Primary 14J50; Secondary 14J26
Published electronically:
August 1, 2002
MathSciNet review:
1926853
Fulltext PDF Free Access
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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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 T. Hosoh, Automorphism groups of cubic surfaces, J. Algebra 192 (1997), 651677. MR 99d:14042
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 Y. Kawamata, A generalization of KodairaRamanujam's vanishing theorem, Math. Ann. 261 (1982), 4346. MR 84i:14022
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 M. Koitabashi, Automorphism groups of generic rational surfaces, J. Algebra 116 (1988), 130 142. MR 89f:14045
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 J. Kollar and S. Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134 (1998). MR 2000b:14018
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 Yu. I. Manin, Rational surfaces over perfect fields, II, Math. USSR Sb. 1 (1967), 141168. MR 37:1374
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 Yu. I. Manin, Cubic forms : Algebra, geometry, arithmetic, 2nd ed, NorthHolland Math. Library, 4 (1986), NorthHolland Publ. Co., AmsterdamNew York. MR 87d:11037
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 M. Miyanishi and K. Masuda, Open algebraic surfaces with finite group actions, Transform. Group, to appear.
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 R. Miranda and U. Persson, On extremal rational elliptic surfaces, Math. Z. 193 (1986), 537558. MR 88a:14044
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 K. Oguiso, Automorphism groups in a family of K3 surfaces, math.AG/0104049.
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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/S0002994702030696
PII:
S 00029947(02)030696
Received by editor(s):
March 10, 2002
Published electronically:
August 1, 2002
Article copyright:
© Copyright 2002 American Mathematical Society
