Trianalytic subvarieties of generalized Kummer varieties

Details Trianalytic subvarieties of generalized Kummer varieties Trianalytic subvarieties of generalized Kummer varieties

1998-01-09

arxiv.org/abs/math/9801038v1

Internat. Math. Res. Notices 1998, no. 9, 439--461

Mathematics

Algebraic Geometry

22 pages, LaTeX 2e

Scientific paper

Let $X$ be a hyperkaehler manifold. Trianalytic subvarieties of $X$ are subvarieties which are complex analytic with respect to all complex structures induced by the hyperkaehler structure. Given a 2-dimensional complex torus $T$, the Hilbert scheme $T^{[n]}$ classifying zero-dimensional subschemes of $T$ admits a hyperkaehler structure. A finite cover of $T^{[n]}$ is a product of $T$ and a simply connected hyperkaehler manifold $K^{[n-1]}$, called generalized Kummer variety. We show that for $T$ generic, the corresponding generalized Kummer variety has no trianalytic subvarieties. This implies that a generic deformation of the generalized Kummer variety has no proper complex subvarieties.

Affiliated with

Also associated with

No associations

Rating

Trianalytic subvarieties of generalized Kummer varieties 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 Trianalytic subvarieties of generalized Kummer varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Trianalytic subvarieties of generalized Kummer varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-52565