Explicit birational geometry of 3-folds of general type, II

Abstract

Let $V$ be a complex nonsingular projective 3-fold of general type. We shall give a detailed classification up to baskets of singularities on a minimal model of $V$. We show that the $m$-canonical map of $V$ is birational for all $m\ge 73$ and that the canonical volume $\text{Vol}(V)\ge 1/2660$. When $\chi ({\mathcal{O}}_V)\le 1$, our result is $\text{Vol}(V)\ge 1/420$, which is optimal. Other effective results are also included in the paper.

Updated version, Journal of Differential Geometry (to appear)

References in corpus (1)

• Canonical stability in terms of singularity index for algebraic threefolds

Cited by in corpus (2)

• Parametrization of rational maps on a variety of general type, and the finiteness theorem
• Weighted hypersurfaces with either assigned volume or many vanishing plurigenera