On the geography of Gorenstein minimal 3-folds of general type
Chen, Meng · Hacon, Christopher D.
Original · EN
Let X be a minimal projective Gorenstein 3-fold of general type. We give two applications of an inequality between χ(ωₓ) and pg(X): 1) Assume that the canonical map Φ|ₖₓ| is of fiber type. Let F be a smooth model of a generic irreducible component in the general fiber of Φ|ₖₓ|. Then the birational invariants of F are bounded from above. 2) If X is nonsingular, then c₁³≤ 1/27 c₁c₂+10/3 where c₁, c₂ are Chern invariants of X.
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