On canonically polarized Gorenstein 3-folds satisfying the Noether equality

Abstract

We study canonically polarized Gorenstein $3$-folds with at most terminal singularities and satisfying $K_X^3=\frac{4}{3}{p}_g(X)-\frac{10}{3}$ and $p_g(X)\ge 7$. We characterize the canonical maps of such $3$-folds, describe a structure theorem for the locally factorial ones and completely classify the smooth ones. New examples of canonically polarized smooth $3$-folds with $K_X^3=\frac{4}{3}{p}_g(X)-\frac{10}{3}$ and $p_g(X)\ge 7$ are constructed. These examples are natural extensions of those constructed by M.~Kobayashi.

arXiv commentRevised version, 17 pages

References in corpus (1)

• Minimal threefolds with small slope and the Noether inequality for canonically polarized threefolds

Cited by in corpus (1)

• Varieties of general type with small volumes