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: $K^3\ge 2(2p_g-5)/3$. This inequality is sharp by known examples of M. Kobayashi. 2) Given a minimal 3-fold $X$ of general type with canonical singularities, if $K^3<(3p_g-5)/2$, we show that $X$ must be birationally fibred by curves of genus 2.

20 pages, modified version, to appear in Math. Res. Lett

Cited by in corpus (6)

• The Noether inequality for algebraic threefolds (With an Appendix by János Kollár)
• On canonically polarized Gorenstein 3-folds satisfying the Noether equality
• Inequality of Noether Type for Gorenstein Minimal 3-folds of General Type
• The Noether inequality for Gorenstein minimal 3-folds
• Geography of irregular Gorenstein 3-folds
• The Noether inequality for smooth minimal 3-folds