English

Construction of Hilbert and Quot Schemes

Algebraic Geometry 2007-05-23 v1

Abstract

This is an expository account of Grothendieck's construction of Hilbert and Quot Schemes, following his talk `Techniques de construction et theoremes d'existence en geometrie algebriques IV : les schemas de Hilbert', Seminaire Bourbaki 221 (1960/61), together with further developments by Mumford and by Altman and Kleiman. Hilbert and Quot schemes are fundamental to modern Algebraic Geometry, in particular, for deformation theory and moduli constructions. These notes are based on a series of six lectures in the summer school `Advanced Basic Algebraic Geometry', held at the Abdus Salam International Centre for Theoretical Physics, Trieste, in July 2003.

Keywords

Cite

@article{arxiv.math/0504590,
  title  = {Construction of Hilbert and Quot Schemes},
  author = {Nitin Nitsure},
  journal= {arXiv preprint arXiv:math/0504590},
  year   = {2007}
}

Comments

36 pages

R2 v1 2026-07-22T17:18:44.957Z