Surfaces with simple geodesics through a point

We study compact connected surfaces inm-dimensional Euclidean spaceE ^m (3 m 5) with a point through which every geodesic is aW-curve regarded as a curve in E^m.     

Generalized evaluation subgroups of product spaces relative to a factor

For any -complexes and , we show that . We use this fact to compute generalized evaluation subgroups of generalized tori relative to a sphere.

     

The Chow rings for 3-dimensional toric varieties with one bad isolated singularity

The properties of a toric variety have strong connection with the combinatorial structure of the corresponding fan and the relations among the generators. Using this fact, we have described explicitly the Chow ring for aQ-factorial toric variety as the Stanley-Reisner ring for the corresponding fan modulo the linear equivalence relation. In this paper, we calculate the Chow ring for 3-dimensionalQ-factorial toric varieties having one bad isolated singularity.