Higher Stanley–Reisner rings and toric residues
نویسندگان
چکیده
منابع مشابه
Higher 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.
متن کاملToric 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 کاملOn Toric Face Rings
Following a construction of Stanley we consider toric face rings associated to rational pointed fans. This class of rings is a common generalization of the concepts of Stanley–Reisner and affine monoid algebras. The main goal of this article is to unify parts of the theories of Stanley–Reisnerand affine monoid algebras. We consider (nonpure) shellable fan’s and the Cohen–Macaulay property. More...
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 کاملRationality for Generic Toric Rings
We study generic toric rings. We prove that they are Golod rings, so the Poincaré series of the residue field is rational. We classify when such a ring is Koszul, and compute its rate. Also resolutions related to the initial ideal of the toric ideal with respect to reverse lexicographic order are described.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2004
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x04000831