In connection with his counterexample to the fourteenth problem of Hilbert, Nagata formulated a conjecture concerning the postulation of r fat points of the same multiplicity in P 2 and proved it when r is a square. Iarrobino formulated a similar conjecture in P d. We prove Iarrobino's conjecture when r is a d-th power. As a corollary, we obtain new counterexamples modeled on those by Nagata.

The history of the production of glass paperweights is obscure as is the history of glass making, the latter being traceable back to the fourteenth and fifteenth centuries B.C. Though the idea of the glass paperweight originated in Venice the main decorative element, the millefiori cane, which ensured its popularity, was Egyptian in origin. The first glass paperweights contained ceramic figures...

0

The American Association for the Advancement of MINNIE B. K. HARRIS. Arcuate Mountains ProScience: duced by Modification of Stone 's Structure MaThe Fourteenth Annual Meeting of the Pacific chine: R. H. MITCHELL and ALAN STONE . .................. 275 Division: DR. J. MURRAY LUCK ........... ............. 255 Special Articles: Obituary: The Relation of Total Nitrogen to Regeneration in Recent D...

Hilbert’s fourteenth problem asks whether the ring of invariants of any representation of a linear algebraic group is finitely generated over the base field. Nagata gave the first counterexample, using a representation of (Ga) 13, where Ga denotes the additive group [22]. In his example, the representation is defined over a field of large transcendence degree over the prime field (of any charac...