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DC Field | Value | Language |
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dc.contributor.author | Favale, F. | - |
dc.contributor.author | Naranjo del Val, Juan Carlos | - |
dc.contributor.author | Pirola, G. P. | - |
dc.date.accessioned | 2019-10-24T13:09:17Z | - |
dc.date.available | 2019-10-24T13:09:17Z | - |
dc.date.issued | 2018-08 | - |
dc.identifier.issn | 0046-5755 | - |
dc.identifier.uri | http://hdl.handle.net/2445/143059 | - |
dc.description.abstract | Let f:S⟶B be a non-trivial fibration from a complex projective smooth surface S to a smooth curve B of genus b. Let cf the Clifford index of the general fibre F of f. In Barja et al. (Journal für die reine und angewandte Mathematik, 2016) it is proved that the relative irregularity of f, qf=h1,0(S)−b is less or equal than or equal to g(F)−cf . In particular this proves the (modified) Xiao's conjecture: qf≤g(F)2+1 for fibrations of general Clifford index. In this short note we assume that the general fiber of f is a plane curve of degree d≥5 and we prove that qf≤g(F)−cf−1 . In particular we obtain the conjecture for families of quintic plane curves. This theorem is implied for the following result on infinitesimal deformations: let F a smooth plane curve of degree d≥5 and let ξ be an infinitesimal deformation of F preserving the planarity of the curve. Then the rank of the cup-product map H0(F,ωF)⟶⋅ξH1(F,OF) is at least d−3 . We also show that this bound is sharp. | - |
dc.format.extent | 9 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Springer Verlag | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1007/s10711-017-0283-4 | - |
dc.relation.ispartof | Geometriae Dedicata, 2018, vol. 195, num. 1, p. 193-201 | - |
dc.relation.uri | https://doi.org/10.1007/s10711-017-0283-4 | - |
dc.rights | (c) Springer Verlag, 2018 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Corbes planes | - |
dc.subject.other | Plane curves | - |
dc.title | On the Xiao conjecture for plane curves | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 673276 | - |
dc.date.updated | 2019-10-24T13:09:17Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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673276.pdf | 153.3 kB | Adobe PDF | View/Open |
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