Journal of Algebraic Geometry

Author(s): Jacopo Stoppa
Journal: J. Algebraic Geom. 19 (2010), 1-17.
Posted: December 8, 2008
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be a polarised manifold. We show that K-stability and asymptotic Chow stability of the blowup of

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.

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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

PII: S 1056-3911(08)00503-1
Received by editor(s): June 26, 2007
Received by editor(s) in revised form: October 8, 2007
Posted: 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.

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