On surfaces of general type with q=5
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 4, pp. 999-1007.

We prove that a complex surface S with irregularity q(S)=5 that has no irrational pencil of genus >1 has geometric genus p g (S)8. As a consequence, we are able to classify minimal surfaces S of general type with q(S)=5 and p g (S)<8. This result is a negative answer, for q=5, to the question asked in [13] of the existence of surfaces of general type with irregularity q that have no irrational pencil of genus >1 and with the lowest possible geometric genus p g =2q-3 (examples are known to exist only for q=3,4).

Publié le :
Classification : 14J29
Lopes, Margarida Mendes 1 ; Pardini, Rita 2 ; Pirola, Gian Pietro 3

1 Departamento de Matemática Universidade Técnica de Lisboa Av. Rovisco Pais 1049-001 Lisboa, Portugal
2 Dipartimento di Matematica Università di Pisa Largo B. Pontecorvo, 5 56127 Pisa, Italy
3 Dipartimento di Matematica Università di Pavia Via Ferrata, 1 27100 Pavia, Italy
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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, Série 5, Tome 11 (2012) no. 4, pp. 999-1007. http://www.numdam.org/item/ASNSP_2012_5_11_4_999_0/

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