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Birational geometry of quartic 3-folds II: The importance of being -factorial

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The paper explores the birational geometry of terminal quartic 3-folds. In doing this I develop a new approach to study maximal singularities with positive dimensional centers. This allows to determine the pliability of a -factorial quartic with ordinary double points, and it shows the importance of -factoriality in the context of birational geometry of uniruled 3-folds.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100, Ferrara, Italy

    Massimiliano Mella

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  1. Massimiliano Mella
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Correspondence to Massimiliano Mella.

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Mathematics Subject Classification (1991): 14E07, 14J30, 14E30

Partially supported by EAGER and ‘‘Geometria sulle Varietà Algebriche’’ (MIUR).

Revised version: 2 January 2004

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Mella, M. Birational geometry of quartic 3-folds II: The importance of being -factorial. Math. Ann. 330, 107–126 (2004). https://doi.org/10.1007/s00208-004-0542-1

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