Talk:Quot scheme

Todo

 * http://algant.eu/documents/theses/habibi.pdf
 * https://arxiv.org/pdf/math/0504590.pdf
 * https://arxiv.org/pdf/1903.08787.pdf
 * https://mathoverflow.net/questions/234037/components-of-kontsevich-moduli-space-of-stable-maps-and-multiple-covers — Preceding unsigned comment added by Wundzer (talk • contribs) 20:23, 27 February 2020 (UTC)

Examples

 * Add example of Grassmannian of a coherent sheaf => quot generalizes the grassmannian
 * Serre correspondence
 * Moduli of semi-stable sheaves on an algebraic curve

Deformation theory
There should be a section about the deformation theory of the quot scheme. This should definitely mention the derived quot scheme and its derived tangent space.

Moduli of sheaves

 * https://arxiv.org/abs/1809.05738
 * https://arxiv.org/abs/alg-geom/9502020 (moduli of sheaves on moduli of curves)
 * https://userpage.fu-berlin.de/hoskins/moduli_and_GIT.html / https://web.archive.org/web/20200301001913/https://userpage.fu-berlin.de/hoskins/M15_Lecture_notes.pdf
 * https://arxiv.org/abs/math/0703214 — Preceding unsigned comment added by Wundzer (talk • contribs) 00:25, 1 March 2020 (UTC)

Curve counting

 * https://arxiv.org/abs/0707.2348
 * https://smf.emath.fr/publications/systemes-coherents-et-structures-de-niveau
 * https://dspace.mit.edu/handle/1721.1/28826 — Preceding unsigned comment added by Wundzer (talk • contribs) 06:53, 3 March 2020 (UTC)

Grassmanian confusion
I am confused by your grassmannian example. You appear to have the k dimensional subspaces as a quotient of a rank k trivial bundle $$\mathcal{O}_{G(n,k)}^{\oplus k} \to \mathcal{U}$$. Do you not want to identify the families of subspaces of dimension k with quotients of a trivial bundle of rank n mapping onto a bundle of rank n-k ?