Displaying similar documents to “Equivariant vector bundles on toric varieties and some problems of linear algebra”

Equivariant principal bundles for G–actions and G–connections

Indranil Biswas, S. Senthamarai Kannan, D. S. Nagaraj (2015)

Complex Manifolds

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Given a complex manifold M equipped with an action of a group G, and a holomorphic principal H–bundle EH on M, we introduce the notion of a connection on EH along the action of G, which is called a G–connection. We show some relationship between the condition that EH admits a G–equivariant structure and the condition that EH admits a (flat) G–connection. The cases of bundles on homogeneous spaces and smooth toric varieties are discussed.

Algebraic cobordism of bundles on varieties

Y.-P. Lee, Rahul Pandharipande (2012)

Journal of the European Mathematical Society

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The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over ℚ ) of the corresponding cobordism groups over Spec( ℂ ) for all dimensions of varieties and ranks of bundles. The basis consists of split bundles over products of projective spaces. Moreover, we prove the full theory for bundles on varieties is an extension of scalars of standard algebraic cobordism.

Wedderburn components, the index theorem and continuous Castelnuovo-Mumford regularity for semihomogeneous vector bundles

Nathan Grieve (2021)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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We study the property of continuous Castelnuovo-Mumford regularity, for semihomogeneous vector bundles over a given Abelian variety, which was formulated in A. Küronya and Y. Mustopa [Adv. Geom. 20 (2020), no. 3, 401-412]. Our main result gives a novel description thereof. It is expressed in terms of certain normalized polynomial functions that are obtained via the Wedderburn decomposition of the Abelian variety’s endomorphism algebra. This result builds on earlier work of Mumford and...

Representation stability for syzygies of line bundles on Segre–Veronese varieties

Claudiu Raicu (2016)

Journal of the European Mathematical Society

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The rational homology groups of packing complexes are important in algebraic geometry since they control the syzygies of line bundles on projective embeddings of products of projective spaces (Segre–Veronese varieties). These complexes are a common generalization of the multidimensional chessboard complexes and of the matching complexes of complete uniform hypergraphs, whose study has been a topic of interest in combinatorial topology. We prove that the multivariate version of representation...