Academic Commons

Theses Doctoral

Derived Categories of Moduli Spaces of Semistable Pairs over Curves

Potashnik, Natasha

The context of this thesis is derived categories in algebraic geometry and geo- metric quotients. Specifically, we prove the embedding of the derived category of a smooth curve of genus greater than one into the derived category of the moduli space of semistable pairs over the curve. We also describe closed cover conditions under which the composition of a pullback and a pushforward induces a fully faithful functor. To prove our main result, we give an exposition of how to think of general Geometric Invariant Theory quotients as quotients by the multiplicative group.

Files

  • thumnail for Potashnik_columbia_0054D_13219.pdf Potashnik_columbia_0054D_13219.pdf binary/octet-stream 373 KB Download File

More About This Work

Academic Units
Mathematics
Thesis Advisors
de Jong, Aise Johan
Degree
Ph.D., Columbia University
Published Here
April 4, 2016
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.