Uniform bundles on quadrics
Xinyi Fang, Duo Li, Yanjie Li

TL;DR
This paper investigates the structure and splitting properties of uniform bundles on quadrics and related homogeneous varieties, establishing new splitting criteria, classifying minimal rank bundles, and partially confirming a conjecture on bundle splitting.
Contribution
It proves the non-existence of certain constant morphisms, improves splitting bounds for uniform bundles, classifies minimal rank bundles on specific homogeneous spaces, and addresses a conjecture on splitting types.
Findings
Only constant morphisms exist from certain quadrics to Grassmannians when conditions are met.
Uniform bundles of rank at most 2m on certain quadrics split, improving previous bounds.
Classified all minimal rank uniform bundles on specific homogeneous varieties.
Abstract
We show that there exist only constant morphisms from to if is even and is not . As an application, we prove on and , any uniform bundle of rank at most splits, which improves the upper bound of splitting for uniform bundles obtained by Kachi and Sato. We classify all unsplit uniform bundles of minimal rank on and . We partially answer a conjecture of Ellia, which predicts that some uniform bundles of special splitting types on necessarily split and we find some restrictions on the splitting types of unsplit uniform bundles of minimal rank.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · advanced mathematical theories · Polynomial and algebraic computation
