On the geography of Gorenstein minimal 3-folds of general type

Details On the geography of Gorenstein minimal 3-folds of general type On the geography of Gorenstein minimal 3-folds of general type

2006-02-25

arxiv.org/abs/math/0602567v1

Mathematics

Algebraic Geometry

To appear in Asian J. Math

Scientific paper

Let $X$ be a minimal projective Gorenstein 3-fold of general type. We give two applications of an inequality between $\chi (\omega_X)$ and $p_g(X)$: 1) Assume that the canonical map $\Phi_{|K_X|}$ is of fiber type. Let $F$ be a smooth model of a generic irreducible component in the general fiber of $\Phi_{|K_X|}$. Then the birational invariants of $F$ are bounded from above. 2) If $X$ is nonsingular, then $c_1^3\leq {1/27} c_1c_2+{10/3}$ where $c_1$, $c_2$ are Chern invariants of $X$.

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