Stability of special instanton bundles on 𝑃²ⁿ⁺¹

Ancona, Vincenzo; Ottaviani, Giorgio

doi:10.1090/S0002-9947-1994-1136544-9

Stability of special instanton bundles on $\textbf {P}^ {2n+1}$
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by Vincenzo Ancona and Giorgio Ottaviani

Trans. Amer. Math. Soc. 341 (1994), 677-693

DOI: https://doi.org/10.1090/S0002-9947-1994-1136544-9

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Abstract:

We prove that the special instanton bundles of rank $2n$ on ${\mathbb {P}^{2n + 1}}(\mathbb {C})$ with a symplectic structure studied by Spindler and Trautmann are stable in the sense of Mumford-Takemoto. This implies that the generic special instanton bundle is stable. Moreover all instanton bundles on ${\mathbb {P}^5}$ are stable. We get also the stability of other related vector bundles.

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