Mathematical Research Letters

Volume 2 (1995)

Number 6

Bounding curves in algebraic surfaces by genus and Chern numbers

Pages: 663 – 676



Steven Shin-Yi Lu (University of Waterloo)

Yoichi Miyaoka (Kyoto University)


This note will provide some effective bounds for the degree of a curve in an algebraic surface of general type with only constraints on the number of ordinary nodes and ordinary triple points of the curve. The degree is taken with respect to the canonical polarization of the surface and the bounds are given linearly in terms of the genus of the curve and the Chern numbers of the surface.

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