Open AccessSlopes of trigonal fibred surfaces and of higher dimensional fibrations
Author(s) -
Barja Miguel A.,
Lidia Stoppino
Publication year - 2009
Publication title -
annali della scuola normale superiore di pisa. classe di scienze
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.444
H-Index - 37
eISSN - 2036-2145
pISSN - 0391-173X
DOI - 10.2422/2036-2145.2009.4.02
Subject(s) - fibered knot , mathematics , surjective function , trigonal crystal system , conjecture , quotient , combinatorics , ample line bundle , dimension (graph theory) , mathematical analysis , pure mathematics , geometry , crystallography , chemistry , crystal structure
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; in particular this result proves a conjecture due to Harris and Stankova-Frenkel