A q-analog of the Fibonacci numbers via complete quadrics

Details A q-analog of the Fibonacci numbers via complete quadrics A q-analog of the Fibonacci numbers via complete quadrics

2010-10-29

arxiv.org/abs/1010.6119v1

Mathematics

Algebraic Geometry

14 pages, 1 figure

Scientific paper

We analyze the fixed variety Y_n of a special unipotent element acting on the space of (n-1)-dimensional complete quadrics. We find a cell decomposition of Y_n, and compute its Poincare polynomial. The cells are indexed by compositions of n with odd parts and the Poincare polynomial of Y_n is a q-analog of the n'th Fibonacci number. We characterize the containment relations of the cell closures combinatorially and find a recurrence for the number of irreducible components of Y_n.

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