We prove that a numerical Godeaux surface cannot have an automorphism of order three.
@article{ASNSP_2008_5_7_3_483_0,
author = {Palmieri, Eleonora},
title = {Automorphisms of order three on numerical {Godeaux} surfaces},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {483--543},
year = {2008},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 7},
number = {3},
mrnumber = {2466438},
zbl = {1183.14054},
language = {en},
url = {https://www.numdam.org/item/ASNSP_2008_5_7_3_483_0/}
}
TY - JOUR AU - Palmieri, Eleonora TI - Automorphisms of order three on numerical Godeaux surfaces JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2008 SP - 483 EP - 543 VL - 7 IS - 3 PB - Scuola Normale Superiore, Pisa UR - https://www.numdam.org/item/ASNSP_2008_5_7_3_483_0/ LA - en ID - ASNSP_2008_5_7_3_483_0 ER -
%0 Journal Article %A Palmieri, Eleonora %T Automorphisms of order three on numerical Godeaux surfaces %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2008 %P 483-543 %V 7 %N 3 %I Scuola Normale Superiore, Pisa %U https://www.numdam.org/item/ASNSP_2008_5_7_3_483_0/ %G en %F ASNSP_2008_5_7_3_483_0
Palmieri, Eleonora. Automorphisms of order three on numerical Godeaux surfaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 3, pp. 483-543. https://www.numdam.org/item/ASNSP_2008_5_7_3_483_0/
[1] , and , “Compact Complex Surfaces”, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3 Folge, Band 4, Springer-Verlag, Berlin, 1984. | Zbl | MR
[2] , and , Complex surfaces of general type: some recent progress, In: “Global aspects of complex geometry”, F. Catanese et al. (eds.), Springer Verlag, 2006, 1-58. | Zbl | MR
[3] , “Rivestimenti del Piano. Sulla Razionalità dei Piani Doppi e Tripli Ciclici”, Edizioni Plus - Pisa University Press, 2006.
[4] , and , Even sets of four nodes on rational surfaces, Math. Res. Lett. 11 (2004), 799-808. | Zbl | MR
[5] , and , Numerical Godeaux surfaces with an involution, Trans. Amer. Math. Soc. 359 (2007), 1605-1632. | Zbl | MR
[6] and , Fibrations of low genus, I, Ann. Sci. Ècole Norm. Sup. 39 (2006), 1011-1049. | Zbl | MR | Numdam
[7] , “Le superficie Algebriche”, Zanichelli, Bologna, 1949. | Zbl | MR
[8] , Sulle curve riducibili appartenenti ad una superficie algebrica, In: “Alfredo Franchetta, Opere Scelte”, C. Ciliberto and E. Sernesi (eds.), Giannini, Napoli, 2006, 139-161. | Zbl | MR
[9] , Sur une surface algébrique de genre zero et de bigenre deux, Atti Accad. Naz. Lincei 14 (1931), 479-481. | Zbl
[10] and , Fixed locus of an involution acting on a Godeaux surface, Math. Proc. Cambridge Philos. Soc. 129 (2000), 205-216. | Zbl | MR
[11] , Triple covers in algebraic geometry, Amer. J. Math. 107 (1985), 1123-1158. | Zbl | MR
[12] , Tricanonical maps of Godeaux surfaces, Invent. Math. 34 (1976), 99-111. | Zbl | MR
[14] , “Numerical Godeaux Surfaces with an Automorphism of Order Three”, Ph.D. thesis, Università degli studi Roma Tre, 2007.
[13] , Abelian covers of algebraic varieties, J. Reine Angew. Math. 417 (1991), 191-213. | Zbl | MR
[15] , Surfaces with , J. Fac. Sci. Univ. Tokio, Sect. IA Math., 25 (1978), 75-92. | Zbl | MR
[16] , On Campedelli branch loci, Ann. Univ. Ferrara, Sez. VII, 43 (1997), 1-26. | Zbl | MR
[17] , Galois triple covers of surfaces, Sci. China, Ser. A, 34 (1991), 935-942. | Zbl | MR
[18] , Bound of automorphisms of surfaces of general type. I, Ann. of Math. (2) 139 (1994), 51-77. | Zbl | MR
[19] , Bound of automorphisms of surfaces of general type. II, J. Algebraic Geom. 4 (1995), 701-793. | Zbl | MR
[20] , On Abelian automorphism group of a surface of general type, Invent. Math. 102 (1990), 619-631. | Zbl | MR
