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A classification of equivariant principal bundles over nonsingular toric varieties
TLDR
In this article, the authors classify holomorphic and algebraic torus equivariant principal bundles over a nonsingular toric variety, where the principal is a complex linear algebraic group.Abstract:
We classify holomorphic as well as algebraic torus equivariant principal $G$-bundles over a nonsingular toric variety $X$, where $G$ is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric variety admits a trivialization in equivariant sense. We also obtain some splitting results.read more
Citations
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Tannakian classification of equivariant principal bundles on toric varieties
TL;DR: In this paper, the notion of compatible ∑-filtered vector space was introduced, where ∑ denotes the fan of a toric variety and G a reductive algebraic group defined over an algebraically closed field.
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Stability of equivariant vector bundles over toric varieties
TL;DR: In this paper, Batyrev et al. gave a complete answer to the question of (semi)stability of tangent bundle of any nonsingular projective complex toric variety with Picard number 2 by using combinatorial crietrion of an equivariant sheaf.
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On equivariant Serre problem for principal bundles
TL;DR: In this paper, a Γ-equivariant algebraic principal G-bundle over a normal complex affine variety X equipped with an action of Γ, where G and Γ are complex linear algebraic groups.
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Toric principal bundles, piecewise linear maps and buildings
Kiumars Kaveh,Christopher Manon +1 more
TL;DR: In this paper, the authors define the notion of piecewise linear maps from a fan of a toric vector bundle to the underlying space of the Tits building of a linear algebraic group.
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Toric bundles, valuations, and tropical geometry over semifield of piecewise linear functions
Kiumars Kaveh,Christopher Manon +1 more
TL;DR: In this article, the notion of a valuation with values in the semifield of piecewise linear functions was introduced, and the Klyachko classification of toric vector bundles was extended.
References
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Book
Introduction to Toric Varieties.
TL;DR: In this article, a mini-course is presented to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications, concluding with Stanley's theorem characterizing the number of simplicies in each dimension in a convex simplicial polytope.
Book
Introduction to toric varieties
TL;DR: The Geometry and Topology of Singularities course as discussed by the authors was based on a previous course given during the 23o Coloquio Brasileiro de Matematica (Rio de Janeiro, July 2001).
Journal ArticleDOI
Varieties of small codimension in projective space
TL;DR: In this paper, it was shown that a subvariety of a nonsingular submodality of dimension r is a complete intersection if and only if its homogeneous prime ideal I(Y)^k[x0, • • •, xn] can be generated by exactly n-r homogeneous polynomials.