Projective 3-folds of general type with X=1

Abstract

There are many examples of 3-folds of general type with $\chi (\mathcal{O})=1$ found by Iano-Fletcher and Reid about twenty years ago. Iano-Fletcher has ever proved $P_{12}(X)\ge 1$ and $P_{24}(X)\ge 2$ for all minimal 3-folds $X$ of general type with $\chi ({\mathcal{O}}_X)=1$. In this paper, we improve on Fletcher's method. Our main result is that ${\varphi }_m$ is birational onto its image for all $m\ge 54$. To prove this we establish a general theory on birationality for general 3-folds which improve known results. Also we will show $P_m\ge 1$ for all $m\ge 14$ and $P_{18}\ge 3$.

updated version, 26 pages

References in corpus (2)

• Explicit birational geometry of threefolds of general type
• Complex projective threefolds with non-negative canonical Euler-Poincare characteristic