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This is a Quantitative Study study.

October 16, 2025Open Access

Some evidence for the existence of Ulrich bundles

Key Points

Existence of ulrich bundles is questioned using K-theoretic and derived category frameworks, suggesting multiple approaches.
If a motivic vector bundle is algebraic, solutions exist within the grothendieck group, pointing to K-theory's role.
Considering derived categories, formal methods for producing ulrich sheaves on surfaces are implied, enhancing potential applications.
This exploration indicates a dual method approach may yield insights into the structure of ulrich bundles in algebraic geometry.

Abstract

The question of existence of Ulrich bundles on nonsingular projective varieties is posed here in weaker terms: either to find a K-theoretic solution, or to find one in the derived category of the variety. We observe that if any motivic vector bundle is algebraic, there is always a solution in the Grothendieck group. Also, by considering the derived problem, it is noted a formal way of producing Ulrich sheaves on a surface.

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Cite This Study

Stefan Deaconu (Tue,) studied this question.

synapsesocial.com/papers/68f0f51d8dd8ea469b1d6d92 https://doi.org/https://doi.org/10.48550/arxiv.2502.18250

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