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Working paper

Minifolds and Phantoms

arxiv.org. math. Cornell University, 2013. No. 1305.4549v1.
Galkin S., Katzarkov L., Mellit A., Shinder E.
A minifold is a smooth projective $n$-dimensional variety such that its bounded derived category of coherent sheaves $\D^b(X)$ admits a semi-orthogonal decomposition into an exceptional collection of $n+1$ exceptional objects. In this paper we classify minifolds of dimension $n \leq 4$. We discuss the structure of the derived category of fake projective spaces and conjecture that under some conditions they admit a quasi-phantom subcategory.