scholarly journals Spectral expansions of random sections of homogeneous vector bundles

2019 ◽  
Vol 97 ◽  
pp. 151-165 ◽  
Author(s):  
A. Malyarenko
Keyword(s):  
Vector Bundles ◽  
Spectral Expansions ◽  
Random Sections ◽  
Homogeneous Vector

scholarly journals Fano 3-folds from homogeneous vector bundles over Grassmannians

2021 ◽  
Author(s):  
Lorenzo De Biase ◽  
Enrico Fatighenti ◽  
Fabio Tanturri
Keyword(s):  
Vector Bundles ◽  
Homogeneous Vector

AbstractWe rework the Mori–Mukai classification of Fano 3-folds, by describing each of the 105 families via biregular models as zero loci of general global sections of homogeneous vector bundles over products of Grassmannians.

scholarly journals Homogeneous vector bundles on homogeneous spaces

Topology ◽  
1972 ◽  
Vol 11 (2) ◽  
pp. 199-203 ◽  
Author(s):  
Harsh V. Pittie
Keyword(s):  
Vector Bundles ◽  
Homogeneous Spaces ◽  
Homogeneous Vector

scholarly journals BALANCED METRICS ON HOMOGENEOUS VECTOR BUNDLES

2011 ◽  
Vol 08 (07) ◽  
pp. 1433-1438 ◽  
Author(s):  
ROBERTO MOSSA
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Holomorphic Vector Bundle ◽  
Kähler Manifold ◽  
Balanced Metrics ◽  
Kahler Manifold ◽  
Balanced Metric ◽  
Compact Kähler Manifold ◽  
Homogeneous Variety ◽  
Homogeneous Vector

Let E → M be a holomorphic vector bundle over a compact Kähler manifold (M, ω) and let E = E1 ⊕ ⋯ ⊕ Em → M be its decomposition into irreducible factors. Suppose that each Ej admits a ω-balanced metric in Donaldson–Wang terminology. In this paper we prove that E admits a unique ω-balanced metric if and only if [Formula: see text] for all j, k = 1,…, m, where rj denotes the rank of Ej and Nj = dim H0(M, Ej). We apply our result to the case of homogeneous vector bundles over a rational homogeneous variety (M, ω) and we show the existence and rigidity of balanced Kähler embedding from (M, ω) into Grassmannians.

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