Geodesic
Slopes of trigonal fibred surfaces and of higher dimensional fibrations
Barja, Miguel Ángel1 ; Stoppino, Lidia2
1 Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, ETSEIB Avda. Diagonal, 08028 Barcelona, Spain
2 Dipartimento di Fisica e Matematica, Università dell’Insubria - Como, Via Valleggio, 11, 22100 Como, Italy
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 647-658

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We give lower bounds for the slope of higher dimensional fibrations f:X⟶B over curves under conditions of GIT-semistability of the fibres, using a generalization of a method of Cornalba and Harris. With the same method we establish a sharp lower bound for the slope of trigonal fibrations of even genus and general Maroni invariant; this result in particular proves a conjecture due to Harris and Stankova-Frenkel.

Classification : 14J10, 14J29, 14D06

Barja, Miguel Ángel 1 ; Stoppino, Lidia 2

1 Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, ETSEIB Avda. Diagonal, 08028 Barcelona, Spain
2 Dipartimento di Fisica e Matematica, Università dell’Insubria - Como, Via Valleggio, 11, 22100 Como, Italy 
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     title = {Slopes of trigonal fibred surfaces and of higher dimensional fibrations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {647--658},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {4},
     year = {2009},
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     zbl = {1204.14017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_4_647_0/}
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Barja, Miguel Ángel; Stoppino, Lidia. Slopes of trigonal fibred surfaces and of higher dimensional fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 647-658. http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_4_647_0/