The phantom-category conjecture for degenerations of quadric bundles

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Consider a degeneration of a generic quadric bundle over a surface. Let Db(−)D^b(-) denote the bounded derived category, and let a phantom category mean a nontrivial category with trivial K0K^0 group.

Quadric-bundle phantom-category conjecture. The semiorthogonal decomposition of the derived category of such a degeneration contains a phantom category.

The conjecture is presented as a mechanism for producing phantom categories through degeneration and is linked in the source to nonrationality questions for quadric bundles.

References

Primary source

Ivan Cheltsov, Ludmil Katzarkov and Victor Przyjalkowski, “Birational geometry via moduli spaces”, arXiv:1405.3374 (2014).

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