On the multiplicity of terminal singularities on threefolds

Mathematics – Algebraic Geometry

Scientific paper

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8 pages

Scientific paper

We give the multiplicity of terminal singularities on threefolds by simple
calculation. Then we obtain the best inequalities for the multiplicity and the
index. By using this, we can improve the boundedness number of terminal weak
Q-Fano 3-folds in [KMMT, Theorem 1.2]. Furthermore, we can extended [K, Theorem
3.6] for Fujita freeness conditions to nonhypersurface terminal singularities.

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