Let (X,L) be a polarised manifold. We show that K-stability and as- ymptotic 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 K ̈ahler classes with no constant scalar curvature representatives.
Unstable blowups / Stoppa, Jacopo. - In: JOURNAL OF ALGEBRAIC GEOMETRY. - ISSN 1056-3911. - 19:1(2010), pp. 1-17. [10.1090/S1056-3911-08-00503-1]
Unstable blowups
Stoppa, Jacopo
2010-01-01
Abstract
Let (X,L) be a polarised manifold. We show that K-stability and as- ymptotic 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 K ̈ahler classes with no constant scalar curvature representatives.File in questo prodotto:
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