Normality of general elephants on 3-fold terminal flips

Abstract

We prove that the general elephant $E_{X^{+}}\in |-K_{X^{+}}|$ is normal where $X-->X^{+}$ is a 3-fold terminal flip. Hence $E_{X^{+}}$ has at worst Du Val singularities. As a corollary, there exists no non-Gorenstein singularity of type $cE/2$, $cD/3$, nor $cAx/4$ on the flipped curve $C^{+}$.

arXiv commentThis paper has been withdrawn by the author since the main Theorem is a consequence of Theorem 2.2 in the paper "Classification of three-dimensional flips"