Minimal threefolds with small slope and the Noether inequality for canonically polarized threefolds
Abstract
1) We give a 3-dimensional analogue of M. Noether's inequality for canonically polarized threefolds: K3 2(2pg-5)/3. This inequality is sharp by known examples of M. Kobayashi. 2) Given a minimal 3-fold X of general type with canonical singularities, if K3< (3pg-5)/2, we show that X must be birationally fibred by curves of genus 2.
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