# Rationally connected non-Fano type varieties

Authors
• 1 University of Bayreuth, Mathematisches Institut, Lehrstuhl Mathematik VIII, Universitätsstraße 30, Bayreuth, 95447, Germany , Bayreuth (Germany)
Type
Published Article
Journal
European Journal of Mathematics
Publisher
Springer International Publishing
Publication Date
Nov 28, 2017
Volume
4
Issue
1
Pages
335–355
Identifiers
DOI: 10.1007/s40879-017-0201-1
Source
Springer Nature
Keywords
Varieties of Fano type are very well behaved with respect to the MMP, and they are known to be rationally connected. We study a relation between the classes of rationally connected varieties and varieties of Fano type. It is known that these classes are birationally equivalent in dimension 2. We give examples of rationally connected varieties of dimension ⩾3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\geqslant 3$$\end{document} which are not birational to varieties of Fano type, thereby answering Question 5.2 of Cascini and Gongyo (Saitama Math J 30:27–38, 2013).