Misha Verbitsky Голосов: 1 Адрес блога: http://lj.rossia.org/users/tiphareth/ Добавлен: 2008-01-02 18:18:22 блограйдером Robin_Bad

Trihyperkaehler reduction

2012-01-25 16:22:47 (читать в оригинале)

Вот еще одна лекция в Токио
http://verbit.ru/MATH/TALKS/Reduction-IPMU.pdf
последняя в этом сезоне

Trihyperkaehler reduction

We define a trisymplectic reduction of a trisymplectic
manifold, which is a complexified form of a hyperkaehler
reduction. We prove that the trisymplectic reduction in
the space of regular rational curves on the twistor space
of a hyperkaehler manifold M is compatible with the
hyperkaehler reduction on M. As an application of these
geometric ideas, we consider the ADHM construction of
instantons and show that the moduli space of rank r,
charge c framed instanton bundles on CP^3 is a smooth,
connected, trisymplectic manifold of complex dimension
4rc. In particular, it follows that the moduli space of
rank 2, charge c instanton bundles on CP^3 is a smooth
complex manifold of dimension 8c-3, thus settling a
30-year old conjecture.

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