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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Deformations of rational $T$-varieties

Authors: Nathan Owen Ilten and Robert Vollmert
Journal: J. Algebraic Geom. 21 (2012), 531-562
Published electronically: September 12, 2011
MathSciNet review: 2914803
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Abstract | References | Additional Information

Abstract: We show how to construct certain homogeneous deformations for rational normal varieties with codimension one torus action. This can then be used to construct homogeneous deformations of any toric variety in arbitrary degree. For locally trivial deformations coming from this construction, we calculate the image of the Kodaira-Spencer map. We then show that for a smooth complete toric variety, our homogeneous deformations span the space of first-order deformations.

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Additional Information

Nathan Owen Ilten
Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
Address at time of publication: Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840

Robert Vollmert
Affiliation: Mathematisches Institut, Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Germany

Received by editor(s): September 21, 2009
Received by editor(s) in revised form: December 3, 2010, and January 3, 2011
Published electronically: September 12, 2011