The cone of effective divisors of log varieties after Batyrev
The aim of these notes is to discuss Batyrev's theorem on the structure of the cone of nef curves (or its dual cone, the cone of pseudo-effective divisors) on terminal threefolds. We point out a problem in Batyrev's original proof, and explain a way of fixing it. In order to complete Batyrev's proof, we rely on boundedness of terminal Fano threefolds. For this reason, as it stands, this proof does not generalize to the log terminal case, as it has been claimed in previous papers.