On the geometry of complete intersection toric varieties

On the Geometry of Complete Intersection Toric Varieties

In this paper we give a geometric characterization of the cones of toric varieties that are complete intersections. In particular, we prove that the class of complete intersection cones is the smallest class of cones which is closed under direct sum and contains all simplex cones. Further, we show that the number of the extreme rays of such a cone, which is less than or equal to 2n − 2, is exac...

The Geometry of Toric Varieties

Toric complete intersection codes

In this paper we construct evaluation codes on zero-dimensional complete intersections in toric varieties and give lower bounds for their minimum distance. This generalizes the results of Gold–Little–Schenck and Ballico–Fontanari who considered evaluation codes on complete intersections in the projective space.

On dual toric complete intersection codes

In this paper we study duality for evaluation codes on intersections of d hypersurfaces with given d -dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be quasi-self-dual. In the case of d = 2 it reduces to a combinatorial condition on the Newton polygons. This allows us to give an explicit construction of dual and q...

Intersection Forms of Toric Hyperkähler Varieties

This note proves combinatorially that the intersection pairing on the middle-dimensional compactly supported cohomology of a toric hyperkähler variety is always definite, providing a large number of non-trivial L2 harmonic forms for toric hyperkähler metrics on these varieties. This is motivated by a result of Hitchin about the definiteness of the pairing of L2 harmonic forms on complete hyperk...