ABSTRACT
It is well known that there is a positive relationship between the maximal multiplicity and the length of associated virtual 1-parameter subgroup of a projective hypersurface. In this article, we will define the multiplicity classes of hypersurfaces and construct them from the Hesselink stratification of a Hilbert scheme.
MATHEMATICS SUBJECT CLASSIFICATION:
Notes
1 According to the literature, such a definition of state polytope is obtained from the canonical -action with the canonical linearization twisted by a power of determinant while we are considering the canonical -action. However, such a setup does not changes the situation of our problem in the viewpoint of GIT as we can see in [4, 2.2]. Also, such a definition of state polytope let us observe the symmetry within our problem directly from the picture.