Nagata’s Compactification Theorem for Normal Toric Varieties over a Valuation Ring of Rank One
نویسندگان
چکیده
منابع مشابه
Classification of Normal Toric Varieties over a Valuation Ring of Rank One
Normal toric varieties over a field or a discrete valuation ring are classified by rational polyhedral fans. We generalize this classification to normal toric varieties over an arbitrary valuation ring of rank one. The proof is based on a generalization of Sumihiro’s theorem to this non-noetherian setting. These toric varieties play an important role for tropicalizations. 2010 Mathematics Subje...
متن کاملA Codimension Theorem for Complete Toric Varieties
Let X be a complete toric variety with homogeneous coordinate ring S. In this article, we study the codimension in the critical degree of ideals of S generated by dim(X) + 1 homogeneous elements that don’t vanish simultaneously on X. Introduction In this paper, X will denote a complete toric variety of dimension n. We will work over C, so that the torus of X is (C). The dual lattices will be de...
متن کاملMATRIX VALUATION PSEUDO RING (MVPR) AND AN EXTENSION THEOREM OF MATRIX VALUATION
Let R be a ring and V be a matrix valuation on R. It is shown that, there exists a correspondence between matrix valuations on R and some special subsets ?(MVPR) of the set of all square matrices over R, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. Furthermore, based on Malcolmson’s localization, an alternative proof for t...
متن کاملResolutions for Equivariant Sheaves over Toric Varieties
In this work we construct global resolutions for general coherent equivariant sheaves over toric varieties. For this, we use the framework of sheaves over posets. We develop a notion of gluing of posets and of sheaves over posets, which we apply to construct global resolutions for equivariant sheaves. Our constructions give a natural correspondence between resolutions for reflexive equivariant ...
متن کاملAn 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 X to be interpolated by an algebraic hypersurface with a fixed class in the Picard group of X. Résumé. — Dans la lignée d’un théorème de Wood, on donne des conditions nécessaires et suffisantes pour qu’une famille de germes d’hype...
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: Michigan Mathematical Journal
سال: 2018
ISSN: 0026-2285
DOI: 10.1307/mmj/1508983384