SAGBI bases for the Kernel of certain locally nilpotent K-derivations on polynomial rings.
نویسندگان
چکیده
منابع مشابه
Sagbi Bases of Cox-Nagata Rings
We degenerate Cox–Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration implies the Batyrev–Popov conjecture that these rings are presented by ideals of quadrics. For the blow-up of projective n-space at n + 3 points, sagbi bases of Cox–Nagata rings establish a link between the Verlinde formul...
متن کاملSagbi Bases in Rings of Multiplicative Invariants
Let k be a field and G be a finite subgroup of GLn(Z). We show that the ring of multiplicative invariants k[x±1 1 , . . . , x ±1 n ] G has a finite SAGBI basis if and only if G is generated by reflections.
متن کاملNilpotent Elements in Skew Polynomial Rings
Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...
متن کاملSagbi Bases for Rings of Invariant Laurent Polynomials
Let k be a field, Ln = k[x ±1 1 , . . . , x ±1 n ] be the Laurent polynomial ring in n variables and G be a group of k-algebra automorphisms of Ln. We give a necessary and sufficient condition for the ring of invariants Ln to have a SAGBI basis. We show that if this condition is satisfied then Ln has a SAGBI basis relative to any choice of coordinates in Ln and any term order.
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: The São Paulo Journal of Mathematical Sciences
سال: 2010
ISSN: 2316-9028,1982-6907
DOI: 10.11606/issn.2316-9028.v4i2p177-187