Holomorphic isometric embeddings of the projective space into quadrics

Yasuyuki Nagatomo

doi:10.1007/s10711-022-00689-4

Holomorphic isometric embeddings of the projective space into quadrics

Yasuyuki Nagatomo

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We classify holomorphic isometric embeddings of the projective space into quadrics using the generalization of do Carmo–Wallach theory in Nagatomo [Harmonic maps into Grassmann manifolds, arXiv:mathDG/1408.1504[mathDG], Holomorphic maps into Grassmann manifolds (Harmonic maps into Grassmann manifolds III), Annals of Global analysis and Geometry 60, 33–63 (2021). An explicit description of their moduli spaces up to image and gauge equivalence is provided.

Original language	English
Article number	31
Journal	Geometriae Dedicata
Volume	216
Issue number	3
DOIs	https://doi.org/10.1007/s10711-022-00689-4
Publication status	Published - Jun 2022

Keywords

Complex quadric
Holomorphic isomorphic embeddings
Moduli spaces
Projective space
Vector bundles

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keywords = "Complex quadric, Holomorphic isomorphic embeddings, Moduli spaces, Projective space, Vector bundles",

author = "Yasuyuki Nagatomo",

note = "Funding Information: The author is grateful to Prof. O. Macia for useful conversations. This research is supported by JSPS KAKENHI Grant Number 17K05230. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature B.V.",

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KW - Projective space

KW - Vector bundles

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Holomorphic isometric embeddings of the projective space into quadrics

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