-schemes and toric varieties.
A basis for the non-archimedean holomorphic theta functions.
A criterion for the ideal of a projectively embedded toric surface to be generated by quadrics.
A general Hilbert-Mumford criterion
Let a reductive group act on an algebraic variety . We give a Hilbert-Mumford type criterion for the construction of open -invariant subsets admitting a good quotient by .
A New Index for Polytopes.
Algebraic families of p-adic tori.
Algebraic tori as Nisnevich sheaves with transfers
We relate -equivalence on tori with Voevodsky’s theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.
Almost complex toric manifolds and positive line bundles
Almost set-theoretic complete intersections in characteristic zero.
We present a class of toric varieties V which, over any algebraically closed field of characteristic zero, are defined by codim V +1 binomial equations.
Alpha-invariant of toric line bundles
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 analog of the Fubini-Studi form for two-dimensional toric varieties.
An analogue of convexity for complements of amoebas of varieties of higher codimension, an answer to a question asked by B. Sturmfels.
An equivariant Riemann-Roch theorem for complete, simplicial toric varieties.
An estimate of approximation constants for p-adic and real varities.
An example of an asymptotically Chow unstable manifold with constant scalar curvature
Donaldson proved that if a polarized manifold has constant scalar curvature Kähler metrics in and its automorphism group is discrete, 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 is not discrete.
An interpolation theorem in toric varieties
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 to be interpolated by an algebraic hypersurface with a fixed class in the Picard group of .
Asymptotics of eigensections on toric varieties
Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities for eigensections approaching a semiclassical ray. Here is a normal compact toric variety and 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
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 -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 .
Birational invariants of algebraic varieties.
Bounding the degrees of generators of a homogeneous dimension 2 toric ideal.