Derived Quot schemes
Algebraic Geometry
2007-05-23 v2
Abstract
Realizing a part of the Derived Deformation Theory program, we construct a "derived" analog of the Grothendieck's Quot scheme parametrizing subsheaves in a given coherent sheaf F on a smooth projective variety X. This analog is a differential graded manifold RQuot_h(F) (so it is always smooth in an appropriate sense) whose tangent space at a point represented by a subsheaf K in F, is a cochain complex quasiisomorphic to RHom(K, F/K).
Cite
@article{arxiv.math/9905174,
title = {Derived Quot schemes},
author = {I. Ciocan-Fontanine and M. Kapranov},
journal= {arXiv preprint arXiv:math/9905174},
year = {2007}
}
Comments
46 pages, AMS-TeX. Revised version, to appear in Ann. Sci. ENS