deformation theory

Tags: #todo

deformation theory

References

https://www.msri.org/summer_schools/419
An overview of classical deformation theory:

attachments/sernesioverviewdefth 1.pdf

Topics

moduli stack of abelian varieties
- a stack is a category fibered in groupoids
moduli space
moduli space
scheme
Schlessinger’s criterion
deformation-obstruction theory
perfect obstruction theory
moduli space
Universal family
pro-representability
local to global spectral sequence
flat morphism
relative differentials
cotangent complex
local complete intersection
nilpotent thickening
formally smooth

Notes

attachments/Pasted%20image%2020211002190654.png

Links to this page

unresolved links output

Schlessinger’s criterion in Unsorted/deformation theory

deformation-obstruction theory in Quick_Notes/2021-10-05 quick_notes, -Unsorted/deformation theory

local to global spectral sequence in Unsorted/deformation theory

moduli stack of abelian varieties in Quick_Notes/2021-04-18, -Quick_Notes/2021-04-23, -Unsorted/Tate module, -Unsorted/deformation theory, -Unsorted/moduli stack of elliptic curves, -Unsorted/stacks MOC

nilpotent thickening in Unsorted/deformation theory

pro-representability in Unsorted/deformation theory
cotangent complex

Relation to dg Lie algebras and deformation theory: deformation theory is controlled by dg Lie algebras.
Lagrangian Floer homology

For closed varieties \(X\), there are techniques due to Seidel for studying it via the theory on \(Y = X\setminus\Sigma_0\) and deformation theory, which has been carried out for the quartic surface and genus 2 curves.