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In this paper it is shown that the extension ideals of polynomial prime and primary ideals in the corresponding ring of entire functions remain prime or primary, respectively. Moreover, we will prove that a primary decomposition of a polynomial ideal can be extended componentwise to a primary decomposition of the extended ideal. In order to show this we… (More)
We prove the following generalization of an example of Hartshorne:
We compare, for smooth monomial projective curves, the Castel-nuovo-Mumford regularity and the reduction number; we present an example where these two numbers differ. However, we show they coincide for a certain class of monomial curves. Furthermore, for smooth monomial curves we prove an inequality which is stronger than the one from the Eisenbud-Goto… (More)
Bounds for the maximal degree of certain Gröbner bases of simplicial toric ideals are given. These bounds are close to the bound stated in Eisenbud-Goto's Conjecture on the Castelnuovo-Mumford regularity.
It is known that a variety in projective space is uniquely determined by its Cayley–van der Waerden–Chow form. An algebraic formulation and a proof (for an arbitrary base field) of this classical result are given in view of applications to the Stückrad–Vogel intersection cycle.