A generalized Bogomolov-Gieseker inequality for the smooth quadric threefold (Q2922858)
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scientific article; zbMATH DE number 6355591
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A generalized Bogomolov-Gieseker inequality for the smooth quadric threefold |
scientific article; zbMATH DE number 6355591 |
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A generalized Bogomolov-Gieseker inequality for the smooth quadric threefold (English)
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15 October 2014
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Bogomolov-Gieseker inequality
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threefolds
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quadrid threefold
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Bridgeland stability conditions
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strong full exceptional collection
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derived category
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The author gives a proof of a Bogomolov-Gieseker inequality proposed in [\textit{A. Bayer} et al., J. Algebr. Geom. 23, No. 1, 117--163 (2014; Zbl 1306.14005)] on a smooth quadric threefold \(Q\). This implies the existence of a family of Bridgeland stability conditions. For this result as essential ingredient it is used a strong full exceptional collection for \(D^b(Q)\) whose existence is due to [\textit{M. M. Kapranov}, Invent. Math. 92, No. 3, 479--508 (1988; Zbl 0651.18008)].
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