Let V be a finite dimensional representation of a p-group, G, over a field, k, of characteristic p. We show that there exists a choice of basis and monomial order for which the ring of invariants, k[V ]G, has a finite SAGBI basis. We describe two algorithms for constructing a generating set for k[V ]G. We use these methods to analyse k[2V3]3 where U3 is the p-Sylow subgroup of GL3(Fp) and 2V3 i...

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...

We introduce canonical bases for subalgebras of quotients of the commutative and non-commutative polynomial ring. The usual theory for Gröbner bases and its counterpart for subalgebras of polynomial rings, also called SAGBI bases, are combined to obtain a tool for computation in subalgebras of factor algebras.

We present families of tableaux which interpolate between the classical semi-standard Young and matching field tableaux. Algebraically, this corresponds to SAGBI bases Plücker algebras . show that each such family leads a toric ideal, can be realized as initial hence degeneration for flag variety.

Given a polynomial ring P over field K , an element g ∈ and -subalgebra S of we deal with the problem saturating respect to i.e. computing Sat ( ) = [ − 1 ] ∩ . In general case describe procedure/algorithm compute set generators for which terminates if only it is finitely generated. Then consider more interesting when graded. particular, graded by positive matrix W indeterminate, show that choo...