Analytic Disks and the Projective Hull
| dc.creator | Lawson Jr., H. Blaine | |
| dc.creator | Wermer, John | |
| dc.date | 2008-06-29 | |
| dc.date | 2008-08-21 | |
| dc.date.accessioned | 2026-07-07T09:57:26Z | |
| dc.date.available | 2026-07-07T09:57:26Z | |
| dc.description | 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. | |
| dc.description | Minor misprints have been corrected | |
| dc.identifier | https://arxiv.org/abs/0806.4776 | |
| dc.identifier | http://arxiv.org/abs/0806.4776 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167342 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.subject | 30H05, 32A38, 32Q99 | |
| dc.title | Analytic Disks and the Projective Hull | |
| dc.type | text |