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- W624194493 abstract "Dolgachev surfaces are simply connected minimal elliptic surfaces with $p_g=q=0$ and of Kodaira dimension 1. These surfaces were constructed by logarithmic transformations of rational elliptic surfaces. In this paper, we explain the construction of Dolgachev surfaces via $mathbb Q$-Gorenstein smoothing of singular rational surfaces with two cyclic quotient singularities. This construction is based on the paper by Lee-Park. Also, some exceptional bundles on Dolgachev surfaces associated with $mathbb Q$-Gorenstein smoothing are constructed based on the idea of Hacking. In the case if Dolgachev surfaces were of type $(2,3)$, we describe the Picard group and present an exceptional collection of maximal length. Finally, we prove that the presented exceptional collection is not full, hence there exist a nontrivial phantom category in the derived category." @default.
- W624194493 created "2016-06-24" @default.
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- W624194493 date "2015-06-17" @default.
- W624194493 modified "2023-09-27" @default.
- W624194493 title "Exceptional collections on Dolgachev surfaces associated with degenerations" @default.
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- W624194493 doi "https://doi.org/10.48550/arxiv.1506.05213" @default.
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