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A general Hilbert-Mumford criterion

Jürgen Hausen (2003)

Annales de l’institut Fourier

Let a reductive group G act on an algebraic variety X . We give a Hilbert-Mumford type criterion for the construction of open G -invariant subsets V X admitting a good quotient by G .

Algebraic tori as Nisnevich sheaves with transfers

Bruno Kahn (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

We relate R -equivalence on tori with Voevodsky’s theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.

Alpha-invariant of toric line bundles

Thibaut Delcroix (2015)

Annales Polonici Mathematici

We generalize the work of Jian Song by computing the α-invariant of any (nef and big) toric line bundle in terms of the associated polytope. We use the analytic version of the computation of the log canonical threshold of monomial ideals to give the log canonical threshold of any non-negatively curved singular hermitian metric on the line bundle, and deduce the α-invariant from this.

An example of an asymptotically Chow unstable manifold with constant scalar curvature

Hajime Ono, Yuji Sano, Naoto Yotsutani (2012)

Annales de l’institut Fourier

Donaldson proved that if a polarized manifold ( V , L ) has constant scalar curvature Kähler metrics in c 1 ( L ) and its automorphism group Aut ( V , L ) is discrete, ( V , L ) is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where Aut ( V , L ) is not discrete.

An interpolation theorem in toric varieties

Martin Weimann (2008)

Annales de l’institut Fourier

In the spirit of a theorem of Wood, we give necessary and sufficient conditions for a family of germs of analytic hypersurfaces in a smooth projective toric variety X to be interpolated by an algebraic hypersurface with a fixed class in the Picard group of X .

Asymptotics of eigensections on toric varieties

A. Huckleberry, H. Sebert (2013)

Annales de l’institut Fourier

Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities | ϕ n | 2 = | s N | 2 / | | s N | | L 2 2 for eigensections s N Γ ( X , L N ) approaching a semiclassical ray. Here X is a normal compact toric variety and L is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate and Zelditch....

Binomial residues

Eduardo Cattani, Alicia Dickenstein, Bernd Sturmfels (2002)

Annales de l’institut Fourier

A binomial residue is a rational function defined by a hypergeometric integral whose kernel is singular along binomial divisors. Binomial residues provide an integral representation for rational solutions of A -hypergeometric systems of Lawrence type. The space of binomial residues of a given degree, modulo those which are polynomial in some variable, has dimension equal to the Euler characteristic of the matroid associated with A .

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