2007-11-02
Tim Goldberg, Cornell University
Convexity theorems from positive Hermitian line bundles
In their 1982 paper proving the abelian convexity theorem, Guillemin
and Sternberg also proved the nonabelian convexity theorem in a
specialized case, where the manifold is K\"ahler and admits a
compatible holomorphic positive Hermitian line bundle. By refining
their techniques, Brion (1986), O'Shea and Sjamaar (2000), Guillemin
and Sjamaar (2006), and the speaker (2007) have obtained convexity
results for the moment images of various algebraic subsets of the
K\"ahler manifold.
I will discuss the setups, statements, and proofs of these results.