Automorphisms of order three on numerical Godeaux surfaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 7 (2008) no. 3, pp. 483-543.

We prove that a numerical Godeaux surface cannot have an automorphism of order three.

Classification: 14J29, 14J50, 14E20
@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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 7},
     number = {3},
     year = {2008},
     mrnumber = {2466438},
     zbl = {1183.14054},
     language = {en},
     url = {http://archive.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  - http://archive.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 http://archive.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, Serie 5, Volume 7 (2008) no. 3, pp. 483-543. http://archive.numdam.org/item/ASNSP_2008_5_7_3_483_0/

[1] W. Barth, C. Peters and A. Van De Ven, “Compact Complex Surfaces”, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3 Folge, Band 4, Springer-Verlag, Berlin, 1984. | MR | Zbl

[2] I. Bauer, F. Catanese and R. Pignatelli, Complex surfaces of general type: some recent progress, In: “Global aspects of complex geometry”, F. Catanese et al. (eds.), Springer Verlag, 2006, 1-58. | MR | Zbl

[3] A. Calabri, “Rivestimenti del Piano. Sulla Razionalità dei Piani Doppi e Tripli Ciclici”, Edizioni Plus - Pisa University Press, 2006.

[4] A. Calabri, C. Ciliberto and M. Mendes Lopes, Even sets of four nodes on rational surfaces, Math. Res. Lett. 11 (2004), 799-808. | MR | Zbl

[5] A. Calabri, C. Ciliberto and M. Mendes Lopes, Numerical Godeaux surfaces with an involution, Trans. Amer. Math. Soc. 359 (2007), 1605-1632. | MR | Zbl

[6] F. Catanese and R. Pignatelli, Fibrations of low genus, I, Ann. Sci. Ècole Norm. Sup. 39 (2006), 1011-1049. | Numdam | MR | Zbl

[7] F. Enriques, “Le superficie Algebriche”, Zanichelli, Bologna, 1949. | MR | Zbl

[8] A. Franchetta, Sulle curve riducibili appartenenti ad una superficie algebrica, In: “Alfredo Franchetta, Opere Scelte”, C. Ciliberto and E. Sernesi (eds.), Giannini, Napoli, 2006, 139-161. | MR | Zbl

[9] L. Godeaux, Sur une surface algébrique de genre zero et de bigenre deux, Atti Accad. Naz. Lincei 14 (1931), 479-481. | Zbl

[10] J. Keum and Y. Lee, Fixed locus of an involution acting on a Godeaux surface, Math. Proc. Cambridge Philos. Soc. 129 (2000), 205-216. | MR | Zbl

[11] R. Miranda, Triple covers in algebraic geometry, Amer. J. Math. 107 (1985), 1123-1158. | MR | Zbl

[12] Y. Miyaoka, Tricanonical maps of Godeaux surfaces, Invent. Math. 34 (1976), 99-111. | MR | Zbl

[14] E. Palmieri, “Numerical Godeaux Surfaces with an Automorphism of Order Three”, Ph.D. thesis, Università degli studi Roma Tre, 2007.

[13] R. Pardini, Abelian covers of algebraic varieties, J. Reine Angew. Math. 417 (1991), 191-213. | MR | Zbl

[15] M. Reid, Surfaces with p g =0,K 2 =1, J. Fac. Sci. Univ. Tokio, Sect. IA Math., 25 (1978), 75-92. | MR | Zbl

[16] E. Stagnaro, On Campedelli branch loci, Ann. Univ. Ferrara, Sez. VII, 43 (1997), 1-26. | MR | Zbl

[17] S. L. Tan, Galois triple covers of surfaces, Sci. China, Ser. A, 34 (1991), 935-942. | MR | Zbl

[18] G. Xiao, Bound of automorphisms of surfaces of general type. I, Ann. of Math. (2) 139 (1994), 51-77. | MR | Zbl

[19] G. Xiao, Bound of automorphisms of surfaces of general type. II, J. Algebraic Geom. 4 (1995), 701-793. | MR | Zbl

[20] G. Xiao, On Abelian automorphism group of a surface of general type, Invent. Math. 102 (1990), 619-631. | MR | Zbl