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Найдены 4 публикации
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Статья
Kishimoto T., Yuri Prokhorov, Zaidenberg M. Osaka Journal of Mathematics. 2014. Vol. 51. No. 4. P. 1093-1113.

We address the following question: When an affine cone over a smooth Fano threefold admits an effective action of the additive group? In this paper we deal with Fano threefolds of index 1 and Picard number 1. Our approach is based on a geometric criterion from our previous paper, which relates the existence of an additive group action on the cone over a smooth projective variety X with the existence of an open polar cylinder in X. Non-trivial families of Fano threefolds carrying a cylinder were found in loc. cit. Here we provide new such examples.

Добавлено: 10 октября 2013
Статья
Ayzenberg A. Osaka Journal of Mathematics. 2015.
Добавлено: 24 сентября 2015
Статья
Verbitsky M. Osaka Journal of Mathematics. 2010. Vol. 47. No. 2. P. 353-384.
Let (M; I; J;K; g) be a hyperkahler manifold, dimRM = 4n. We study positive, @-closed (2p; 0)-forms on (M; I). These forms are quaternionic analogues of the positive (p; p)-forms, well-known in complex geometry. We construct a monomorphism Vp;p : 2p;0 I (M) 􀀀!n+p;n+p I (M), which maps @-closed (2p; 0)-forms to closed (n+p; n+p)-forms, and positive (2p; 0)- forms to positive (n + p; n + p)-forms. This construction is used to prove a hyperkahler version of the classical Skoda-El Mir theorem, which says that a trivial extension of a closed, positive current over a pluripolar set is again closed. We also prove the hyperkahler version of the Sibony's lemma, showing that a closed, positive (2p; 0)-form de ned outside of a compact complex subvariety Z  (M; I), codimZ > 2p is locally integrable in a neighbourhood of Z. These results are used to prove polystability of derived direct images of certain coherent sheaves.
Добавлено: 12 октября 2012
Статья
Ayano T. Osaka Journal of Mathematics. 2014. Vol. 51. No. 2. P. 459-481.
Добавлено: 2 ноября 2016