We prove that a complex surface with irregularity that has no irrational pencil of genus has geometric genus . As a consequence, we are able to classify minimal surfaces of general type with and . This result is a negative answer, for , to the question asked in [13] of the existence of surfaces of general type with irregularity that have no irrational pencil of genus and with the lowest possible geometric genus (examples are known to exist only for ).
@article{ASNSP_2012_5_11_4_999_0, author = {Lopes, Margarida Mendes and Pardini, Rita and Pirola, Gian Pietro}, title = {On surfaces of general type with $q=5$}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {999--1007}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {4}, year = {2012}, mrnumber = {3060707}, zbl = {1272.14030}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2012_5_11_4_999_0/} }
TY - JOUR AU - Lopes, Margarida Mendes AU - Pardini, Rita AU - Pirola, Gian Pietro TI - On surfaces of general type with $q=5$ JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 999 EP - 1007 VL - 11 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_4_999_0/ LA - en ID - ASNSP_2012_5_11_4_999_0 ER -
%0 Journal Article %A Lopes, Margarida Mendes %A Pardini, Rita %A Pirola, Gian Pietro %T On surfaces of general type with $q=5$ %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 999-1007 %V 11 %N 4 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_4_999_0/ %G en %F ASNSP_2012_5_11_4_999_0
Lopes, Margarida Mendes; Pardini, Rita; Pirola, Gian Pietro. On surfaces of general type with $q=5$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 4, pp. 999-1007. http://archive.numdam.org/item/ASNSP_2012_5_11_4_999_0/
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