Inequality of Noether Type for Gorenstein Minimal 3-folds of General Type

Abstract

Let $X$ be a Gorenstein minimal $3$-fold of general type. We prove the optimal inequality: $$K_X^3\ge \frac{4}{3}\chi ({\omega }_X)-2,$$ where $\chi ({\omega }_X)$ is the Euler-Poincar$\acute{\text{e}}$ characteristic of the dualizing sheaf ${ø}_X$.

9 pages, Comm. Anal. Geom. (to appear)

References in corpus (2)

• Explicit resolution of three dimensional terminal singularities
• Minimal threefolds with small slope and the Noether inequality for canonically polarized threefolds

Cited by in corpus (1)

• Relative Clifford inequality for varieties fibered by curves