## Journal of Symplectic Geometry

### Scaling limits for equivariant Szego kernels

Roberto Paoletti

#### Abstract

Suppose that the compact and connected Lie group $G$ acts holomorphically on the irreducible complex projective manifold $M$, and that the action linearizes to the Hermitian ample line bundle $L$ on $M$. Assume that $0$ is a regular value of the associated moment map. The spaces of global holomorphic sections of powers of $L$ may be decomposed over the finite dimensional irreducible representations of $G$. We study how the holomorphic sections in each equivariant piece asymptotically concentrate along the zero locus of the moment map. In the special case where $G$ acts freely on the zero locus of the moment map, this relates the scaling limits of the Szego kernel of the quotient to the scaling limits of the invariant part of the Szego kernel of $(M,L)$.

#### Article information

Source
J. Symplectic Geom., Volume 6, Number 1 (2008), 9-32.

Dates
First available in Project Euclid: 2 July 2008

https://projecteuclid.org/euclid.jsg/1215032731

Mathematical Reviews number (MathSciNet)
MR2417438

Zentralblatt MATH identifier
1146.53061

#### Citation

Paoletti, Roberto. Scaling limits for equivariant Szego kernels. J. Symplectic Geom. 6 (2008), no. 1, 9--32. https://projecteuclid.org/euclid.jsg/1215032731