Mathematical Research Letters

Volume 13, Issue 4, July 2006 pp. 653-666.

The Noether inequality for smooth minimal 3-folds

Authors: Fabrizio Catanese (1), Meng Chen (2), and De-Qi Zhang (3)
Author institution: Fudan University (1), Fudan University (2), and National University of Singapore (3)

Summary: 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.

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