Holomorphic curves in surfaces of general type.

Abstract:

:This note answers some questions on holomorphic curves and their distribution in an algebraic surface of positive index. More specifically, we exploit the existence of natural negatively curved "pseudo-Finsler" metrics on a surface S of general type whose Chern numbers satisfy c(2)1>2c2 to show that a holomorphic map of a Riemann surface to S whose image is not in any rational or elliptic curve must satisfy a distance decreasing property with respect to these metrics. We show as a consequence that such a map extends over isolated punctures. So assuming that the Riemann surface is obtained from a compact one of genus q by removing a finite number of points, then the map is actually algebraic and defines a compact holomorphic curve in S. Furthermore, the degree of the curve with respect to a fixed polarization is shown to be bounded above by a multiple of q - 1 irrespective of the map.

authors

Lu SS,Yau ST

doi

10.1073/pnas.87.1.80

keywords:

subject

Has Abstract

pub_date

1990-01-01 00:00:00

pages

80-2

issue

1

eissn

0027-8424

issn

1091-6490

journal_volume

87

pub_type

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