José Luis González

Some non-finitely generated Cox rings

We give a large family of weighted projective planes, blown up at a smooth point, that do not have finitely generated Cox rings. We then use the method of Castravet and Tevelev to prove that the moduli space of stable n-pointed genus zero curves does not have a finitely generated Cox ring if n is at least 13.

Projectivized Rank Two Toric Vector Bundles are Mori Dream Spaces

We prove that the Cox ring of the projectivization P(ℰ) of a rank two toric vector bundle ℰ, over a toric variety X, is a finitely generated k-algebra. As a consequence, P(ℰ) is a Mori dream space if the toric variety X is projective and simplicial.

Bivariant algebraic cobordism

We associate a bivariant theory to any suitable oriented Borel-Moore homology theory on the category of algebraic schemes or the category of algebraic G-schemes. Applying this to the theory of algebraic cobordism yields operational cobordism rings and operational G-equivariant cobordism rings associated to all schemes in these categories. In the case of toric varieties, the operational T-equivariant cobordism ring may be described as the ring of piecewise graded power series on the fan with coefficients in the Lazard ring.

Biocarbon ureterostomy device for urinary diversion Multicenter clinical trial

The bioCarbon ureterostomy device is a stomal prosthesis for upper tract urinary diversion that has had preliminary successes in animal and human trials in Europe and Peru. Implantation of a pure carbon stomal prosthesis offers the potential advantages of high biocompatibility, lack of encrustation, and elimination of stomal stenosis which is frequently associated with cutaneous ureterostomy. Nine bioCarbon ureterostomy devices were implanted from August, 1984 through July, 1985. Although successful implantation was achieved in 2 patients, the complication rate was high. The bioCarbon ureterostomy device has potential as an alternative form of urinary diversion. However, significant problems need to be remedied before it can be recommended for routine clinical application.

Projectivity in Algebraic Cobordism

The algebraic cobordism group of a scheme is generated by cycles that are proper morphisms from smooth quasiprojective varieties. We prove that over a field of characteristic zero the quasiprojectivity assumption can be omitted to get the same theory.