On a Conjecture of Harvey and Lawson

Details On a Conjecture of Harvey and Lawson On a Conjecture of Harvey and Lawson

2008-07-23

arxiv.org/abs/0807.3583v1

Mathematics

Complex Variables

Scientific paper

We consider complex projective space P^{n} and a smooth closed curve gamma in P^{n}. Harvey and Lawson have defined the notion of the projective hull \hat{K} of a compact subset K in P^n. This concept is an analogue of the polynomial hull of compact subsets of C^{n}. In the present note we study the relation between the following two properties of the curve gamma: (1) \hat{gamma} - gamma is a one-dimensional complex analytic subvariety of P^{n} - gamma, and (2) There exists a Stein subdomain of P^{n} which contains the projective hull \hat{gamma} of gamma.

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