# GIT lecture 17

This lecture ( GIT17-18) was given on 10/5/09

### Excerpts

Before it was disscussed how if you had a torus acting on a vector space then (semi)stability could be tested by checking if was in the cone of certain characters (forming the support; see prev. lectures). This lecture discusses another criterion for (semi)stability. Namely you look at the torus in . And look at the lattice of one parameter subgroups

In the case a point is represented by a homogeneous poly of degree d, say f. Then you look at and say its unstable if for some choice of coordinates there exists such that for all . Chance to and to to get conditions for semi stability and stability.

The rest of the lecture looks in particular at degree 3 forms and singular points on it.

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- Published:
- October 12, 2009 / 6:42 pm

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- GIT (course)

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