Timeline for Why we study Geometric invariant theory?

7 events

when toggle format	what		by	license	comment
May 3, 2015 at 19:48	history	edited	user9072		added tag
May 3, 2015 at 18:11	answer	added	coudy		timeline score: 19
May 3, 2015 at 16:59	comment	added	David Benjamin Lim		One reason for studying GIT would be the construction of quotients (and hence of various types of moduli spaces). Mumford showed that if $X \subseteq \Bbb{P}(V)$ is a projective variety with $V$ a linear representation of a linearly reductive group $G$, such that $G$ acts on $X$ via restriction, then a good quotient of the semistable locus $X^{ss}$ exists. This idea was used by Mumford, Gieseker, etc to prove that a coarse moduli space $M_g$ exists. Nowadays, there are more fancy methods to prove this coarse moduli space exists, such as the Keel-Mori Theorem.
May 3, 2015 at 16:19	review	Close votes
May 3, 2015 at 19:48
May 3, 2015 at 16:10	comment	added	Yemon Choi		Would "it is interesting and rich" count as a "reason for studying GIT"? (I think that if this question stays open then it would be helpful to have a better idea of the kind of answer you want.)
May 3, 2015 at 15:59	review	First posts
May 3, 2015 at 16:01
May 3, 2015 at 15:57	history	asked	riu_ss	CC BY-SA 3.0