Fano varieties with large pseudoindex and non-free rational curves
Kiwamu Watanabe

TL;DR
This paper classifies certain Fano varieties with large pseudoindex and non-free rational curves, extending previous classifications and exploring relationships between invariants.
Contribution
It provides a classification of extremal contractions for Fano varieties with large pseudoindex and non-free rational curves, and completes the classification for cases with higher Picard number.
Findings
Classification of extremal contractions for these Fano varieties
Complete classification of Fano n-folds with pseudoindex ≥ n-2 and Picard number > 1
Relations between pseudoindex and other invariants of Fano varieties
Abstract
For , let be a complex smooth Fano -fold whose minimal anticanonical degree of non-free rational curves on is at least . 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 -folds with pseudoindex at least 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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Vietnamese History and Culture Studies · Advanced Numerical Analysis Techniques
