منابع مشابه
Toric Residues
In this paper, we will show how these properties of residues can be generalized to an arbitrary projective toric variety. The paper is organized into six sections as follows. In §1, we define the cohomology class [ωg] ∈ H(P,ΩPn), and then §2 generalizes this to define toric residues in terms of a toric analog of the Trace Property. We recall some commutative algebra associated with toric variet...
متن کاملResidues in toric varieties
We study residues on a complete toric variety X , which are defined in terms of the homogeneous coordinate ring of X . We first prove a global transformation law for toric residues. When the fan of the toric variety has a simplicial cone of maximal dimension, we can produce an element with toric residue equal to 1. We also show that in certain situations, the toric residue is an isomorphism on ...
متن کاملCombinatorial Construction of Toric Residues
The toric residue is a map depending on n + 1 divisors on a complete toric variety of dimension n . It appears in a variety of contexts such as sparse polynomial systems, mirror symmetry, and GKZ hypergeometric functions. In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated po...
متن کاملMixed Toric Residues and Tropical Degenerations
This paper is a follow-up to our paper [19], where we prove a conjecture of Batyrev and Materov, the Toric Residue Mirror Conjecture (TRMC). Here we extend our results, and show that they imply a generalization of this conjecture, the Mixed Toric Residue Mirror Conjecture (MTRMC), which is also due to Batyrev and Materov [3]. Roughly, these conjectures state that the generating function of cert...
متن کاملHigher Stanley–Reisner rings and toric residues
We give a purely algebraic proof of the hypersurface case of the Toric Residue Mirror Conjecture recently proposed by Batyrev and Materov.
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1996
ISSN: 0004-2080
DOI: 10.1007/bf02559508