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July 2022 Equivariant holomorphic embeddings from the complex projective line into complex Grassmannian of 2-planes
Isami Koga, Yasuyuki Nagatomo
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Osaka J. Math. 59(3): 495-514 (July 2022).

Abstract

Using gauge theory, we classify $\text{SU}(2)$-equivariant holomorphic embeddings from $\mathbf CP^1$ with the Fubini-Study metric into Grassmann manifold $\mathit{Gr}_{N-2}(\mathbf C^N)$. It is shown that the moduli spaces of those embeddings are identified with the gauge equivalence classes of non-flat invariant connections satisfying semi-positivity on the vector bundles given by \textit{extensions} of line bundles. A topology on the moduli is obtained by means of $L^2$-inner product on Dolbeault cohomology group to which the extension class belongs. The compactification of the moduli is provided with geometric meaning from viewpoint of maps.

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Isami Koga. Yasuyuki Nagatomo. "Equivariant holomorphic embeddings from the complex projective line into complex Grassmannian of 2-planes." Osaka J. Math. 59 (3) 495 - 514, July 2022.

Information

Received: 27 November 2020; Revised: 23 March 2021; Published: July 2022
First available in Project Euclid: 23 June 2022

Subjects:
Primary: 53C07
Secondary: 32H02

Rights: Copyright © 2022 Osaka University and Osaka City University, Departments of Mathematics

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Vol.59 • No. 3 • July 2022
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