Ample Divisors, Automorphic Forms and Shafarevich's Conjecture

Details Ample Divisors, Automorphic Forms and Shafarevich's Conjecture Ample Divisors, Automorphic Forms and Shafarevich's Conjecture

2000-04-07

arxiv.org/abs/math/0004044v2

Mathematics

Algebraic Geometry

Scientific paper

In this article we give a general approach to the following analogue of Shafarevich's conjecture for some polarized algebraic varieties; suppose that we fix a type of an algebraic variety and look at families of such type of varieties over a fixed Riemann surface with fixed points over which we have singular varieties, then one can ask if the set of such families, up to isomorphism, is finite. In this paper we give a general approach to such types of problems. The main observation is the following; suppose that the moduli space of a fixed type of algebraic polarized variety exists and suppose that in some projective smooth compactification of the coarse moduli the discriminant divisor supports an ample one, then it is not difficult to see that this fact implies the analogue of Shafarevich's conjecture. In this article we apply this method to certain polarized algebraic K3 surfaces and also to Enriques surfaces.

Affiliated with

Also associated with

No associations

Rating

Ample Divisors, Automorphic Forms and Shafarevich's Conjecture 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 Ample Divisors, Automorphic Forms and Shafarevich's Conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ample Divisors, Automorphic Forms and Shafarevich's Conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-586217