The phantom-category conjecture for degenerations of quadric bundles

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.

Sources & referencesView supporting material

Primary source

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

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