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arXiv · 1506.02991

The full exceptional collections of categorical resolutions of curves

Zhaoting Wei
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Abstract

This paper gives a complete answer of the following question: which (singular, projective) curves have a categorical resolution of singularities which admits a full exceptional collection? We prove that such full exceptional collection exists if and only if the geometric genus of the curve equals to 0. Moreover we can also prove that a curve with geometric genus equal or greater than 1 cannot have a categorical resolution of singularities which has a tilting object. The proofs of both results are given by a careful study of the Grothendieck group and the Picard group of that curve.

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Zhaoting Wei. 2015-06-09. The full exceptional collections of categorical resolutions of curves. https://doi.org/10.1016/j.jpaa.2016.02.018

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