BOUNDING VOLUMES OF SINGULAR FANO THREEFOLDS

作者：Lai Ching Jui^*

来源：Nagoya Mathematical Journal, 2016, 224(1): 37-73.

DOI：10.1017/nmj.2016.21

Let (X, Delta) be an n-dimensional is an element of-klt log Q-Fano pair. We give an upper bound for the volume Vol(X, Delta)= (-(K-x + Delta))(n) when n = 2, or n = 3 and X is Q-factorial of rho(X) = 1. This bound is essentially sharp for n = 2. The main idea is to analyze the covering families of tigers constructed in J. M(c)Kernan (Boundedness of log terminal fano pairs of bounded index, preprint, 2002, arXiv: 0205214). Existence of an upper bound for volumes is related to the Borisov-Alexeev-Borisov Conjecture, which asserts boundedness of the set of is an element of-klt log Q-Fano varieties of a given dimension n.

• 出版日期2016-12