TY - ELEC
AU - Puchol, Martin
PY - 2018
TI - G-invariant holomorphic Morse inequalities
LA - eng
M3 - Moving Image
AB - Consider an action of a connected compact Lie group on a compact complex
manifold $M$, and two equivariant vector bundles $L$ and $E$ on $M$,
with $L$ of rank 1. The purpose of this talk is to establish holomorphic
Morse inequalities, analogous to Demailly's one, for the invariant part
of the Dolbeault cohomology of tensor powers of $L$, twisted by $E$. To
do so, we define a moment map $\mu$ by the Kostant formula and then the
reduction of $M$ under a natural hypothesis on $\mu^{-1}(0)$. Our
inequalities are given in term of the curvature of the bundle induced by
$L$ on this reduction, in the spirit of "quantization commutes with
reduction"
N2 - Consider an action of a connected compact Lie group on a compact complex
manifold $M$, and two equivariant vector bundles $L$ and $E$ on $M$,
with $L$ of rank 1. The purpose of this talk is to establish holomorphic
Morse inequalities, analogous to Demailly's one, for the invariant part
of the Dolbeault cohomology of tensor powers of $L$, twisted by $E$. To
do so, we define a moment map $\mu$ by the Kostant formula and then the
reduction of $M$ under a natural hypothesis on $\mu^{-1}(0)$. Our
inequalities are given in term of the curvature of the bundle induced by
$L$ on this reduction, in the spirit of "quantization commutes with
reduction"
UR - https://open.library.ubc.ca/collections/48630/items/1.0372801
ER - End of Reference