Symplectic small deformations of special instanton bundle on \(\mathbb{P}^{2n + 1}\) (Q1570189)
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scientific article; zbMATH DE number 1471607
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Symplectic small deformations of special instanton bundle on \(\mathbb{P}^{2n + 1}\) |
scientific article; zbMATH DE number 1471607 |
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Symplectic small deformations of special instanton bundle on \(\mathbb{P}^{2n + 1}\) (English)
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13 November 2000
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Let \(M\) denote the moduli space of stable symplectic instanton bundles on \(\mathbb{P}^{2n+1}\) with second Chern class \(k\). The author proves that, for \(k\geq 2\), the dimension of the Zariski tangent space \(H^1(S^2E)\) to \(M\) at a special instanton bundle \(E\) is \(2k(5n-1)+ 4n^2-10n+3\). This is non-trivial because the obstruction space \(H^2(S^2E)\) is in general non-zero (although all the other cohomology of \(S^2E\) is zero).
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small deformations
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Yang-Mills equation
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symplectic instanton bundles
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dimension of the Zariski tangent space
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