Stability conditions on product varieties
Stability conditions on product varieties
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发表时间：
2019
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通讯作者：
Yuchen Liu
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作者：
Yuchen Liu
给定光滑射影簇X上的一个稳定性条件，我们构造了X × C {X imes C}，其中C是光滑的射影曲线。特别地，这给出了曲线的任意乘积的稳定性条件的存在性。该证明遵循户田的思想，利用Bayer和Macrandom建立的正引理和D ∈（X × C）{D（X）}中有界t-结构的Abramovich-Polishchuk心的弱稳定性条件 imes C）}。
Abstract Given a stability condition on a smooth projective variety X, we construct a family of stability conditions on X × C {X imes C} , where C is a smooth projective curve. In particular, this gives the existence of stability conditions on arbitrary products of curves. The proof uses, by following an idea of Toda, the positivity lemma established by Bayer and Macrì and weak stability conditions on the Abramovich-Polishchuk heart of a bounded t-structure in D ( X × C ) {D(X imes C)} .