Let G be an affine algebraic group acting on an affine variety X. We present an algorithm for computing generators of the invariant ring K[X] in the case where G is reductive. Furthermore, we address the case where G is connected and unipotent, so the invariant ring need not be finitely generated. For this case, we develop an algorithm which computes K[X] in terms of a so-called colon-operation...

Let A be a commutative Noetherian ring, and let R = A[X] be the polynomial ring in an infinite collection X of indeterminates over A. Let SX be the group of permutations of X. The group SX acts on R in a natural way, and this in turn gives R the structure of a left module over the left group ring R[SX ]. We prove that all ideals of R invariant under the action of SX are finitely generated as R[...

judicious use of the SLC linac, damping rings, and positron High-energy ring (HER) Low-energy ring (LER) source.. Particles per bunch ._, -. _ II. ROLE OF R&D PROGRAM IN OVERALL PEP-II INJECTION High-energy ring (HER) Low-energy ring (LER) The overall goals of the PEP-II Injection System are Linac repetition rate summarized in Table 1. These differ from those given in Linac current range during...

In recent years the cohomology ring of the moduli space Ng(2, d) of rank two and odd degree d stable bundles over a Riemann surface M of genus g ≥ 2 has been extensively studied [2], [5], [10], [11]. The subring H(Ng(2, d);Q) Γ of H(Ng(2, d);Q) which is invariant under the induced action of the mapping class group Γ of M has also been much studied and has been shown to play a central role in th...

Using the Frobenius map, we introduce a new invariant for a pair (R, a) of a ring R and an ideal a ⊂ R, which we call the F-pure threshold c(a) of a, and study its properties. We see that the F-pure threshold characterizes several ring theoretic properties. By virtue of Hara and Yoshida’s result [HY], the F-pure threshold c(a) in characteristic zero corresponds to the log canonical threshold lc...

Let G be an affine algebraic group acting on an affine variety X. We present an algorithm for computing generators of the invariant ring K[X] in the case where G is reductive. Furthermore, we address the case where G is connected and unipotent, so the invariant ring need not be finitely generated. For this case, we develop an algorithm which computes K[X] in terms of a so-called colon-operation...

Using the Frobenius map, we introduce a new invariant of a pair (R, a) of a ring R and an ideal a ⊂ R, which we call the F-pure threshold c(a) of a, and study its properties. We see that the F-pure threshold characterizes some ring theoretic properties. By virtue of Hara and Yoshida's result [HY], the F-pure threshold c(a) in characteristic zero corresponds to the log canonical threshold lc(a) ...

Let F = {Fn} be a multiplicative filtration of a local ring such that the Rees algebra R(F) is Noetherian. We recall Burch’s inequality for F and give an upper bound of the a-invariant of the associated graded ring a(G(F)) using a reduction system of F . Applying those results, we study the symbolic Rees algebra of certain ideals of dimension 2.

This paper treats synchronization dynamics in a shift-invariant ring of N mutually coupled self-sustained electrical units. Via some qualitative theory for the Lyapunov exponents, we derive the regimes of coupling parameters for which synchronized oscillation is stable or unstable in the ring.

The supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree, a new invariant of the ring, which is finite provided the ring has finite integral closure. As a consequence, one obtains bounds for the Castelnuovo-Mumford regularity of the Rees algebra and for the Artin-Rees numbers.