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Higher discriminants of vector bundles and Schur functors (2503.15365v1)
Published 19 Mar 2025 in math.AG and math.RT
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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