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On canonically polarized Gorenstein 3-folds satisfying the Noether equality. (English) Zbl 1390.14121

Summary: We study canonically polarized Gorenstein minimal 3-folds satisfying \(K^3_X = \frac{4}{3} p_g (X) - \frac{10}{3}\) and \(p_g (X) \geq 7\). We characterize their canonical maps, describe a structure theorem for such \(3\)-folds and completely classify the smooth ones. New examples of canonically polarized smooth \(3\)-folds with \(K^3_X = \frac{4}{3} p_g (X) - \frac{10}{3}\) and \(p_g (X) \geq 7\) are constructed. These examples are natural extensions of those constructed by M. Kobayashi [J. Math. Soc. Japan 44, No. 1, 145–156 (1992; Zbl 0766.14033)].

MSC:

14J30 \(3\)-folds

Citations:

Zbl 0766.14033
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