Fano visitors, Fano dimension and orbifold Fano hosts
Young-Hoon Kiem, Kyoung-Seog Lee

TL;DR
This paper advances the understanding of Fano visitors and Fano dimensions by establishing a Hodge-theoretic criterion, classifying many varieties as Fano visitors, and exploring derived categories of Fano orbifolds with complex subcategories.
Contribution
It introduces a Hodge-theoretic criterion for Fano hosts, precisely determines Fano dimensions for key examples, and systematically extends the class of known Fano visitors and orbifold derived categories.
Findings
Hodge-theoretic criterion for Fano host existence
Fano dimensions for low genus curves and Calabi-Yau varieties
Examples of Fano orbifolds with complex derived categories
Abstract
In arXiv:1503.00125, the authors proved that every complete intersection smooth projective variety is a Fano visitor, i.e. its derived category is equivalent to a full triangulated subcategory of the derived category of a smooth Fano variety , called a Fano host of . They also introduced the notion of Fano dimension of as the smallest dimension of a Fano host and obtained an upper bound for the Fano dimension of each complete intersection variety. In this paper, we provide a Hodge-theoretic criterion for the existence of a Fano host which enables us to determine the Fano dimensions precisely for many interesting examples, such as low genus curves, quintic Calabi-Yau 3-folds and general complete intersection Calabi-Yau varieties. Next we initiate a systematic search for more Fano visitors. We generalize the methods of arXiv:1503.00125 to prove that…
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models
