Details:
Title  The ring of evenly weighted points on the line.  Author(s)  Milena Hering, Benjamin J. Howard  Type  Article in Journal  Abstract  Let Mw=(ℙ1)n//SL2 denote the geometric invariant theory quotient of (ℙ1)n by the diagonal action of SL2 using the line bundle (w1,w2,…,wn) on (ℙ1)n. Let Rw be the coordinate ring of Mw. We give a closed formula for the Hilbert function of Rw, which allows us to compute the degree of Mw. The graded parts of Rw are certain Kostka numbers, so this Hilbert function computes stretched Kostka numbers. If all the weights wi are even, we find a presentation of Rw so that the ideal Iw of this presentation has a quadratic Gröbner basis. In particular, Rw is Koszul. We obtain this result by studying the homogeneous coordinate ring of a projective toric variety arising as a degeneration of Mw.  Keywords  Invariant theory, Gelfand–Tsetlin polytopes, SAGBI degeneration  ISSN  00255874; 14321823/e 
URL 
http://link.springer.com/article/10.1007%2Fs0020901312724 
Language  English  Journal  Math. Z.  Volume  277  Number  34  Pages  691708  Publisher  Springer, Berlin/Heidelberg  Year  2014  Edition  0  Translation 
No  Refereed 
No 
