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# Communications in Analysis and Geometry

## Volume 17 (2009)

### Number 2

### A quadratic inequality for sum of co-adjoint orbits

Pages: 265 – 282

DOI: http://dx.doi.org/10.4310/CAG.2009.v17.n2.a4

#### Authors

#### Abstract

We obtain an effective lower bound on the distance of thesum of co-adjoint orbits from the origin. Even when thedistance is zero (thus the symplectic quotient is welldefined) our result gives a nontrivial constraint on theseco-adjoint~orbits. In the particular case of unitarygroups, we obtain the quadratic inequality foreigenvalues of Hermitian matrices satisfying\begin{equation*}A+B=C.\end{equation*}This quadratic inequality can be interpreted as the Chern number inequalityfor semi-stable reflexive toric sheaves.