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A Remark on Rationally Connected Varieties and Mori Dream Spaces

Part of: Birational geometry

Published online by Cambridge University Press:  26 September 2018

Claudio Fontanari  and
Diletta Martinelli
Claudio Fontanari*
Affiliation:
Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38123 Povo, Trento, Italy (claudio.fontanari@unitn.it)
Diletta Martinelli
Affiliation:
Diletta Martinelli, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK (Diletta.Martinelli@ed.ac.uk)
*
*Corresponding author.
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Abstract

In this short note, we show that a construction by Ottem provides an example of a rationally connected variety that is not birationally equivalent to a Mori dream space with terminal singularities.

Keywords

Mori dream spacerationally connected varietybirational rigidity

MSC classification

Primary: 14E30: Minimal model program (Mori theory, extremal rays)
Secondary: 14E07: Birational automorphisms, Cremona group and generalizations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 1 , February 2019 , pp. 259 - 263
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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