Redundant blow-ups of rational surfaces with big anticanonical divisor
arXiv:1411.3891
Abstract
We completely classify redundant blow-ups appearing in the theory of rational surfaces with big anticanonical divisor due to Sakai. In particular, we construct a rational surface with big anticanonical divisor which is not a minimal resolution of a del Pezzo surface with only rational singularities, which gives a negative answer to a question raised in a paper by Testa, Várilly-Alvarado, and Velasco.
16 pages. This was part of math.AG/1303.2274, which has been divided into two parts