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EnglishWe 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)>7. As a consequence, one is 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 arXiv:0811.0390 of the existence of surfaces of general type with irregularity q>3 that have no irrational pencil of genus >1 and with the lowest possible geometric genus p_g=2q-3. This gives some evidence for the conjecture that the only irregular surface with no irrational pencil of genus >1 and p_g=2q-3 is the symmetric product of a genus three curve. The research that lead to the present paper was partially supported by a grant of the group GNSAGA of INdAM
On surfaces of general type with q=5 / Mendes Lopes Margarida; Pardini Rita; Pirola Gian Pietro. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - STAMPA. - XI:4(2012), pp. 999-1007.
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| Titolo: | On surfaces of general type with q=5 | |
| Autori: | ||
| Data di pubblicazione: | 2012 | |
| Rivista: | ||
| Citazione: | On surfaces of general type with q=5 / Mendes Lopes Margarida; Pardini Rita; Pirola Gian Pietro. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - STAMPA. - XI:4(2012), pp. 999-1007. | |
| Abstract: | 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)>7. As a consequence, one is 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 arXiv:0811.0390 of the existence of surfaces of general type with irregularity q>3 that have no irrational pencil of genus >1 and with the lowest possible geometric genus p_g=2q-3. This gives some evidence for the conjecture that the only irregular surface with no irrational pencil of genus >1 and p_g=2q-3 is the symmetric product of a genus three curve. The research that lead to the present paper was partially supported by a grant of the group GNSAGA of INdAM | |
| Handle: | http://hdl.handle.net/11571/256313 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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