Splitting of supervector bundles on projective superspaces

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2025年5月14日

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Charles Almeida,
Ugo Bruzzo

摘要

We provide a splitting criterion for supervector bundles over the projective superspaces $\mathbb {P}^{n|m}$ $P^{n | m}$ . More precisely, we prove that a rank p|q supervector bundle on $\mathbb {P}^{n|m}$ $P^{n | m}$ with vanishing intermediate cohomology is isomorphic to the direct sum of even and odd line bundles, provided that $n \ge 2$ $n \geq 2$ . For $n=1$ $n = 1$ we provide an example of a supervector bundle that cannot be written as a sum of line bundles.