The relative pluricanonical stability for 3-folds of general type

This paper aims to improve a theorem of Janos Kollar. For a given Complex projective threefold X of general type, suppose the plurigenus p_k(X)\ge 2, Kollar proved that the (11k+5)-canonical map is birational. Here we show that either the (7k+3)-canonical map or the (7k+5)-canonical map is birational and that the m-canonical map is stably birational for m\ge 13k+6. If P_k(X)\ge 3, then the m-canonical map is stably birational for m\ge 10k+8. In particular, the 12-canonical map is birational when p_g(X)\ge 2 and the 11-canonical map is birational when p_g(X)\ge 3.Comment: 11 pages, new version, Amstex, to appear in Proceedings AM

On canonically derived families of surfaces of general type over curves

Suppose X is a smooth projective 3-fold of general type and |mK_X| is composed of a pencil of surfaces with m>1. This pencil naturally induces a fibration f:X->C onto a smooth curve C after the Stein-factorization, which is the main objects of this article. Based on Koll'ar's earlier works, we improve on it and try to understand the family in terms of discrete birational invariants of the total space as well as those of the general fiber and the base curve. The aim of this note is to build a little bit basic facts.Comment: 19 pages, Amstex, Accepted for publication in Communications in Algebr

Heavy Flavors in High Energy ep Collisions

Most recent measurements of open charm and beauty production in high energy ep collisions at HERA are reviewed. The measurements explored the different aspects of quantum chromodynamics involved in the process of heavy flavor production. The results are compared with perturbative theoretical calculations at next-to-leading order.Comment: 6 pages including figures, to be published in the proceedings of XXXV International Symposium on Multiparticle Dynamics (ISMD), Kromeriz, Czech Republic, August 9-15, 200