Higher discriminants of vector bundles and Schur functors

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This is a Quantitative Study study.

Alessandro D’Andrea; Enrico Fatighenti; Claudio Onorati

doi:10.48550/arxiv.2503.15365

March 19, 2025Open Access

Higher discriminants of vector bundles and Schur functors

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Key Points

Closed formulas for the logarithmic Chern character of locally free sheaves are established, linking geometry and representation theory.
The significant metric includes the connection with Casimir elements of $rak{sl}_r$, demonstrating their role in the formulas.
The method includes a representation-theoretic approach to yield results in the context of vector bundles and Schur functors.
This research provides a pathway to construct slope polystable modular bundles on hyper-Kähler manifolds from existing bundles.

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Abstract

We prove some closed formulas for the logarithmic Chern character of a locally free sheaf. The argument used is representation-theoretic and we connect these formulas with the actions of some Casimir elements of slᵣ. As an application, we give a recipe to construct slope polystable modular bundles on hyper-K\"ahler manifolds from old ones.

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D’Andrea et al. (2025) studied this question.

synapsesocial.com/papers/68e62de1a8c0c6d4587400dc https://doi.org/10.48550/arxiv.2503.15365

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Higher discriminants of vector bundles and Schur functors

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Higher discriminants of vector bundles and Schur functors

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Abstract

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