Equivariant Holomorphic Hermitian Vector Bundles over a Projective Space

Indranil Biswas () and Francois-Xavier Machu
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Indranil Biswas: Department of Mathematics, Shiv Nadar University, NH91, Tehsil Dadri, Greater Noida 201314, Uttar Pradesh, India
Francois-Xavier Machu: Ecole Supérieure d’Informatique Électronique Automatique (ESIEA), 74 bis Av. Maurice Thorez, 94200 Ivry-sur-Seine, France

Mathematics, 2024, vol. 12, issue 23, 1-14

Abstract: The aim here is to describe all isomorphism classes of SU ( n + 1 ) -equivariant Hermitian holomorphic vector bundles on the complex projective space C P n . If G ⊂ SU ( n + 1 ) is the isotropy subgroup of a chosen point x 0 ∈ C P n , and ρ : G ⟶ GL ( V ) is a unitary representation, we obtain SU ( n + 1 ) -equivariant holomorphic Hermitian vector bundles on C P n . Next, given any v ∈ End ( V ρ ) ⊗ ( T z 0 0 , 1 C P n ) ∗ satisfying certain conditions, a new structure of an SU ( n + 1 ) -equivariant holomorphic Hermitian vector bundle on this underlying C ∞ holomorphic Hermitian bundle is obtained. It is shown that all SU ( n + 1 ) -equivariant holomorphic Hermitian vector bundles on C P n arise this way.

Keywords: projective space; equivariant holomorphic Hermitian vector bundle; unitary group (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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