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}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 7}, number = {3}, year = {2008}, mrnumber = {2466438}, zbl = {1183.14054}, language = {en}, url = {http://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 - http://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 http://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. http://www.numdam.org/item/ASNSP_2008_5_7_3_483_0/
[1] “Compact Complex Surfaces”, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3 Folge, Band 4, Springer-Verlag, Berlin, 1984. | MR | Zbl
, and ,[2] 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
, and ,[3] “Rivestimenti del Piano. Sulla Razionalità dei Piani Doppi e Tripli Ciclici”, Edizioni Plus - Pisa University Press, 2006.
,[4] Even sets of four nodes on rational surfaces, Math. Res. Lett. 11 (2004), 799-808. | MR | Zbl
, and ,[5] Numerical Godeaux surfaces with an involution, Trans. Amer. Math. Soc. 359 (2007), 1605-1632. | MR | Zbl
, and ,[6] Fibrations of low genus, I, Ann. Sci. Ècole Norm. Sup. 39 (2006), 1011-1049. | Numdam | MR | Zbl
and ,[7] “Le superficie Algebriche”, Zanichelli, Bologna, 1949. | MR | Zbl
,[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. | MR | Zbl
,[9] Sur une surface algébrique de genre zero et de bigenre deux, Atti Accad. Naz. Lincei 14 (1931), 479-481. | Zbl
,[10] Fixed locus of an involution acting on a Godeaux surface, Math. Proc. Cambridge Philos. Soc. 129 (2000), 205-216. | MR | Zbl
and ,[11] Triple covers in algebraic geometry, Amer. J. Math. 107 (1985), 1123-1158. | MR | Zbl
,[12] Tricanonical maps of Godeaux surfaces, Invent. Math. 34 (1976), 99-111. | MR | Zbl
,[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. | MR | Zbl
,[15] Surfaces with , J. Fac. Sci. Univ. Tokio, Sect. IA Math., 25 (1978), 75-92. | MR | Zbl
,[16] On Campedelli branch loci, Ann. Univ. Ferrara, Sez. VII, 43 (1997), 1-26. | MR | Zbl
,[17] Galois triple covers of surfaces, Sci. China, Ser. A, 34 (1991), 935-942. | MR | Zbl
,[18] Bound of automorphisms of surfaces of general type. I, Ann. of Math. (2) 139 (1994), 51-77. | MR | Zbl
,[19] Bound of automorphisms of surfaces of general type. II, J. Algebraic Geom. 4 (1995), 701-793. | MR | Zbl
,[20] On Abelian automorphism group of a surface of general type, Invent. Math. 102 (1990), 619-631. | MR | Zbl
,