A global Torelli theorem for hyperkahler manifolds

Details A global Torelli theorem for hyperkahler manifolds A global Torelli theorem for hyperkahler manifolds

2009-08-28

arxiv.org/abs/0908.4121v7

Mathematics

Algebraic Geometry

46 pages, version 7.0, addressed a question of Dan Huybrechts about the difference between the Teichmuller space and marked mo

Scientific paper

A mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies. We compute a mapping class group of a hypekahler manifold $M$, showing that it is commensurable to an arithmetic subgroup in SO(3, b_2-3). A Teichmuller space of $M$ is a space of complex structures on $M$ up to isotopies. We define a birational Teichmuller space by identifying certain points corresponding to bimeromorphically equivalent manifolds, and show that the period map gives an isomorphism of the birational Teichmuller space and the corresponding period space $SO(b_2-3, 3)/SO(2)\times SO(b_2 -3, 1)$. We use this result to obtain a Torelli theorem identifying any connected component of birational moduli space with a quotient of a period space by an arithmetic subgroup. When $M$ is a Hilbert scheme of $n$ points on a K3 surface, with $n-1$ a prime power, our Torelli theorem implies the usual Hodge-theoretic birational Torelli theorem (for other examples of hyperkahler manifolds the Hodge-theoretic Torelli theorem is known to be false).

Affiliated with

Also associated with

No associations

Rating

A global Torelli theorem for hyperkahler manifolds 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 A global Torelli theorem for hyperkahler manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A global Torelli theorem for hyperkahler manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-192888