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Quantizations of Fourier- Mukai Transforms
| Content Provider | Semantic Scholar |
|---|---|
| Author | Arinkin, Dima Block, Jonathan Mark Pantev, Tony |
| Copyright Year | 2011 |
| Abstract | We study deformations of Fourier–Mukai transforms in general complex analytic settings. Suppose X and Y are complex manifolds, and let P be a coherent sheaf on X × Y. Suppose that the Fourier–Mukai transform ${\Phi}$Φ given by the kernel P is an equivalence between the coherent derived categories of X and of Y. Suppose also that we are given a formal *-quantization ${\mathbb{X}}$X of X. Our main result is that ${\mathbb{X}}$X gives rise to a unique formal *-quantization ${\mathbb{Y}}$Y of Y. For the statement to hold, *-quantizations must be understood in the framework of stacks of algebroids. The quantization ${\mathbb{Y}}$Y is uniquely determined by the condition that ${\Phi}$Φ deforms to an equivalence between the derived categories of ${\mathbb{X}}$X and ${\mathbb{Y}}$Y . Equivalently, the condition is that P deforms to a coherent sheaf ${\tilde{P}}$P~ on the formal *-quantization ${\mathbb{X} \times\mathbb{Y}^{op}}$X×Yop of X × Y; here ${\mathbb{Y}^{op}}$Yop is the opposite of the quantization ${\mathbb{Y}}$Y . |
| Starting Page | 1403 |
| Ending Page | 1482 |
| Page Count | 80 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00039-013-0233-8 |
| Volume Number | 23 |
| Alternate Webpage(s) | https://www.math.upenn.edu/~blockj/papers/Arinkin2013_Article_-QuantizationsOfFourierMukaiTr.pdf |
| Alternate Webpage(s) | http://www.crm.umontreal.ca/FourierMukaiNahm07/pdf/pantevSlides.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
