Geodesic
The canonical 2-gerbe of a holomorphic vector bundle
Theory and applications of categories, Tome 32 (2017), pp. 1028-1049

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

For each holomorphic vector bundle we construct a holomorphic bundle 2-gerbe that geometrically represents its second Beilinson-Chern class. Applied to the cotangent bundle, this may be regarded as a higher analogue of the canonical line bundle in complex geometry. Moreover, we exhibit the precise relationship between holomorphic and smooth gerbes. For example, we introduce an Atiyah class for gerbes and prove a Koszul-Malgrange type theorem.

Publié le :
Classification : 18F15
Keywords: Holomorphic Gerbes, Second Chern class, Complex manifolds, Holomorphic vector bundles 
@article{TAC_2017_32_a29,
     author = {Markus Upmeier},
     title = {The canonical 2-gerbe of a holomorphic vector bundle},
     journal = {Theory and applications of categories},
     pages = {1028--1049},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a29/}
}
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Markus Upmeier. The canonical 2-gerbe of a holomorphic vector bundle. Theory and applications of categories, Tome 32 (2017), pp. 1028-1049. http://geodesic.mathdoc.fr/item/TAC_2017_32_a29/