Fano varieties with large pseudoindex and non-free rational curves

2023/09/07 by Kiwamu Watanabe, Watanabe, Kiwamu
Mathematics · Social Sciences · Engineering · #Algebraic Geometry and Number Theory #Vietnamese History and Culture Studies #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2309.03438

Abstract

For n≥ 4, let X be a complex smooth Fano n-fold whose minimal anticanonical degree of non-free rational curves on X is at least n-2. We classify extremal contractions of such varieties. As an application, we obtain a classification of Fano fourfolds with pseudoindex and Picard number greater than one. Combining this result with previous results, we complete the classification of smooth Fano n-folds with pseudoindex at least n-2 and Picard number greater than one. This can be seen as a generalization of various previous results. We also discuss the relations between pseudoindex and other invariants of Fano varieties.

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• Classification of smooth Fano varieties with large pseudoindex
• Fano varieties of middle pseudoindex
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