Projective 3-folds of general type with X=1

Details Projective 3-folds of general type with X=1 Projective 3-folds of general type with X=1

2006-11-29

arxiv.org/abs/math/0611898v2

Mathematics

Algebraic Geometry

updated version, 26 pages

Scientific paper

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 $\phi_m$ 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 $P_m\geq 1$ for all $m\geq 14$ and $P_{18}\geq 3$.

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