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.
Citation
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.
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