Mathematics – Algebraic Geometry
Scientific paper
2005-10-14
Mathematics
Algebraic Geometry
28 pages, in French, LaTeX. v2, v3: minor grammatical changes. v4: a proposition (4.8) on potential density over function fiel
Scientific paper
Motivated by an example, due to Voisin, of a smooth simply-connected projective variety with trivial canonical class and cyclic Picard group, admitting a meromorphic endomorphism of high degree, we study meromorphic fibrations on certain varieties with trivial canonical class. We show (theorem 2.1) that any nontrivial meromorphic fibration of a variety with trivial canonical class and cyclic Picard group is in varieties of general type. Therefore, Voisin's endomorphism cannot preserve a fibration, at least in the generic case. As this example is symplectic, we study meromorphic fibrations on symplectic varieties. In dimension 4 (and in all dimensions modulo minimal model program) we get some results similar to Matsushita's. The main result here is theorem 3.6. We also study the relations between meromorphic endomorphisms and meromorphic fibrations. In particular, we prove that if an endomorphism does not preserve a fibration, then its general iterated orbit is Zariski-dense. We show that some power of an endomorphism preserves the "core" (a natural fibration constructed by the second author), and ask the similar question about the Iitaka fibration.
Amerik Ekaterina
Campana Frederic
No associations
LandOfFree
Fibrations meromorphes sur certaines varietes de classe canonique triviale does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fibrations meromorphes sur certaines varietes de classe canonique triviale, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fibrations meromorphes sur certaines varietes de classe canonique triviale will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-223096