Analytic Disks and the Projective Hull

Details Analytic Disks and the Projective Hull Analytic Disks and the Projective Hull

2008-06-29

arxiv.org/abs/0806.4776v2

Mathematics

Complex Variables

Minor misprints have been corrected

Scientific paper

Let X be a complex manifold and c a simple closed curve in X. We address the question: What conditions on c ensure the existence of a 1-dimensional complex subvariety V with boundary c in X. When X = C^n, an answer to this question involves the polynomial hull of gamma. When X = P^n, complex projective space, the projective hull hat{c} of c comes into play. One always has V contained in hat{c}, and for analytic curves they conjecturally coincide. In this paper we establish an approximate analogue of this idea which holds without the analyticity of c. We characterize points in hat{c} as those which lie on a sequence of analytic disks whose boundaries converge down to c. This is in the spirit of work of Poletsky and of Larusson-Sigurdsson, whose work is essential here. The results are applied to construct a remarkable example of a closed curve c in P^2, which is real analytic at all but one point, and for which the closure of hat{c} is W \cup L where L is a projective line and W is an analytic (non-algebraic) subvariety of P^2 - L. Furthermore, hat{c} itself is the union of W with only two points on L.

Affiliated with

Also associated with

No associations

Rating

Analytic Disks and the Projective Hull 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 Analytic Disks and the Projective Hull, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analytic Disks and the Projective Hull will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-259336