Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-24T13:31:23.040Z Has data issue: false hasContentIssue false
  • English
  • Français

Rationality does not specialise among terminal varieties

Published online by Cambridge University Press:  09 February 2016

BURT TOTARO
BURT TOTARO*
Affiliation:
UCLA Mathematics Department, Box 951555, Los Angeles, CA 90095-1555U.S.A. e-mail: totaro@math.ucla.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A limit of rational varieties need not be rational, even when all varieties in the family are projective and have at most terminal singularities.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 1 , July 2016 , pp. 13 - 15
Copyright
Copyright © Cambridge Philosophical Society 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Colliot-Thélène, J. L. and Pirutka, A. Hypersurfaces quartiques de dimension 3: non rationalité stable. Ann. Sci. École Norm. Sup. to appear.Google Scholar
[2]de Fernex, T. and Fusi, D.Rationality in families of threefolds. Rend. Circ. Mat. Palermo 62 (2013), 127–135.CrossRefGoogle Scholar
[3]Hacon, C. and McKernan, J.On Shokurov's rational connectedness conjecture. Duke Math. J. 138 (2007), 119–136.Google Scholar
[4]Kawamata, Y.Deformations of canonical singularities. J. Amer. Math. Soc. 12 (1999), 85–92.Google Scholar
[5]Kollár, J.Rational Curves on Algebraic Varieties (Springer, 1996).Google Scholar
[6]Kollár, J.Singularities of the Minimal Model Program (Cambridge University Press, 2013).Google Scholar
[7]Nakayama, N.Zariski-Decomposition and Abundance (Mathematical Society of Japan, 2004).CrossRefGoogle ScholarPubMed
[8]Totaro, B. Hypersurfaces that are not stably rational. J. Amer. Math. Soc., to appear.Google Scholar
[9]Voisin, C.Unirational threefolds with no universal codimension 2 cycle. Invent. Math. 201 (2015), 207–237.Google Scholar