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arXiv · 1712.01528

A Horrocks' theorem for reflexive sheaves

Laura Costa·Simone Marchesi·Rosa Maria Miró-Roig
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Abstract

In this paper, we define $m$-tail reflexive sheaves as reflexive sheaves on projective spaces with the simplest possible cohomology. We prove that the rank of any $m$-tail reflexive sheaf $\mathcal{E}$ on $\mathcal{P}^n$ is greater or equal to $ nm-m$. We completely describe $m$-tail reflexive sheaves on $\mathcal{P}^n$ of minimal rank and we construct huge families of $m$-tail reflexive sheaves of higher rank.

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Laura Costa, Simone Marchesi, Rosa Maria Miró-Roig. 2017-12-05. A Horrocks' theorem for reflexive sheaves. https://arxiv.org/abs/1712.01528

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