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arXiv · 2503.15365

Higher discriminants of vector bundles and Schur functors

Alessandro D'Andrea·Enrico Fatighenti·Claudio Onorati
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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 $\mathfrak{sl}_r$. 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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Alessandro D'Andrea, Enrico Fatighenti, Claudio Onorati. 2025-03-19. Higher discriminants of vector bundles and Schur functors. https://arxiv.org/abs/2503.15365

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