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The Space of Triangles, Vanishing Theorems, and Combinatorics

✍ Scribed by Wilberd van der Kallen; Peter Magyar

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
207 KB
Volume
222
Category
Article
ISSN
0021-8693

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✦ Synopsis

Ž n . 3 We consider compactifications of P R j ⌬ , the space of triples of distinct i j points in projective space. One such space is a singular variety of configurations of points and lines; another is the smooth compactification of Fulton and MacPherson; and a third is the triangle space of Schubert and Semple. We compute the sections of line bundles on these spaces, and show that they are Ž . equal as GL n representations to the generalized Schur modules associated to Ž . ''bad'' generalized Young diagrams with three rows Borel᎐Weil theorem . On the one hand, this yields Weyl-type character and dimension formulas for the Schur modules; on the other, a combinatorial picture of the space of sections. Cohomology vanishing theorems play a key role in our analysis.

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