Singularities of a threefold having an effective ample divisor which is a smooth surface of Kodaira dimension zero

Our talk is based on a paper of Ivan Cheltsov (http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=1755&option_lang=eng). We prove that a threefold $X$ having an effective ample divisor which is a smooth surface of Kodaira dimension zero is either a contraction of exceptional section $\mathbb{P}(\mathcal{O}_H + \mathcal{O}_H(H))$ or $X$ has only canonical singularities and $H$ is K3 or Enriques surface.