Mathematics – Algebraic Geometry
Scientific paper
2010-10-15
Mathematics
Algebraic Geometry
Scientific paper
The question of higher dimensional Arakelov-Parshin rigidity asks when it is impossible to deform families of canonically polarized manifolds without changing their base. It is one of the three main pieces in higher dimensional Shafarevich conjecture. By a different, already proven piece, for any class of families with fixed Hilbert polynomial, Arakelov-Parshin rigidity yields finiteness of the given class. In the present article rigidity of towers of smooth curve fibrations with genera at least two is examined. In the compact base case, it turns out that, apart form an obvious exception, if any variation is zero, then some cover of the tower can be deformed. In the meanwhile if all variations are non-zero, then the tower is rigid. The arbitrary base case is much more obscure. In that case rigidity is proven for level two towers with maximal variations. The method used there is showing that the iterated Kodaira-Spencer map is injective. In the end this method is related to the infinitesimal Torelli problem. It is shown that if the multiplication map from canonical to bicanonical sections is surjective, then the injectivity of the iterated Kodaira-Spencer map implies the injectivity of the tangent map of the period map.
No associations
LandOfFree
Arakelov-Parshin rigidity of towers of curve fibrations, connections to the infinitesimal Torelli problem 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 Arakelov-Parshin rigidity of towers of curve fibrations, connections to the infinitesimal Torelli problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Arakelov-Parshin rigidity of towers of curve fibrations, connections to the infinitesimal Torelli problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-203407