Abstract
Rational pairs generalize the notion of rational singularities to reduced pairs (X, D). In this paper we deal with the problem of determining whether a normal variety X has a rationalizing divisor, i.e., a reduced divisor D such that (X, D) is a rational pair. We give a criterion for cones to have a rationalizing divisor, and relate the existence of such a divisor to the locus of rational singularities of a variety.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Elkik, Singularités rationnelles et déformations. Inventiones Mathematicae 47(2), 139–147 (1978)
L. Erickson, Deformation invariance of rational pairs. Ph.D. Thesis, University of Washington. USA, (2014)
L. Erickson, Deformation invariance of rational pairs, arXiv preprint arXiv:1407.0110 (2014)
P. Graf, S.J. Kovács, Potentially Du Bois spaces. J. Singul. 8, 117–134 (2014)
R. Hartshorne, Algebraic Geometry, vol. 52 (Springer, Newyork, 1977)
J. Kollár. Singularities of the minimal model program, Cambridge Tracts in Mathematics, vol. 200, Cambridge University Press, Cambridge, with the collaboration of Sándor J Kovács, (2013)
A. Seidenberg, The hyperplane sections of normal varieties. Trans. Am. Math. Soc. 69(2), 357–386 (1950)
Acknowledgements
The author would like to thank his advisor Sándor Kovács for his supervision, direction, and many insights into the subject of this project. The author would also like to thank Siddharth Mathur for numerous useful conversations.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Prelli, L. On rationalizing divisors. Period Math Hung 75, 210–220 (2017). https://doi.org/10.1007/s10998-017-0188-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10998-017-0188-x