Mathematical Research Letters

Volume 13 (2006)

Number 4

The Noether inequality for smooth minimal 3-folds

Pages: 653 – 666



Fabrizio Catanese (Fudan University)

Meng Chen (Fudan University)

De-Qi Zhang (National University of Singapore)


Let $X$ be a smooth projective minimal 3-fold of general type. We prove the sharp inequality $$K_X^3\ge \frac{2}{3}(2p_g(X)-5),$$ an analogue of the classical Noether inequality for algebraic surfaces of general type.

Published 1 January 2006