Unstable blowups

Stoppa, Jacopo

doi:10.1090/S1056-3911-08-00503-1

Unstable blowups

Author: Jacopo Stoppa
Journal: J. Algebraic Geom. 19 (2010), 1-17
DOI: https://doi.org/10.1090/S1056-3911-08-00503-1
Published electronically: December 8, 2008
MathSciNet review: 2551756
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Abstract | References | Additional Information

Abstract: Let $(X,L)$ be a polarised manifold. We show that K-stability and asymptotic Chow stability of the blowup of $X$ along a $0$-dimensional cycle are closely related to Chow stability of the cycle itself, for polarisations making the exceptional divisors small. This can be used to give (almost) a converse to the results of Arezzo and Pacard (2004 and 2007) and to give new examples of Kähler classes with no constant scalar curvature representatives.

References

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Additional Information

Jacopo Stoppa
Affiliation: Università di Pavia, Dipartimento di Matematica “F. Casorati”, Via Ferrata 1, 27100 Pavia, Italy
Address at time of publication: Department of Mathematics, Imperial College, London SW7 2AZ, United Kingdom
Email: jacopo.stoppa@unipv.it

Received by editor(s): June 26, 2007
Received by editor(s) in revised form: October 8, 2007
Published electronically: December 8, 2008
Additional Notes: The author was supported by a Ph.D. Studentship of the University of Pavia and is grateful to Imperial College, London, for the kind hospitality.