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PreprintCC BY 4.0arXiv

The Szegő log-term and local rigidity of Kähler--Einstein polarizations of compact Hermitian symmetric spaces

  • Andrea Loi
  • Matteo Palmieri
  • Fabio Zuddas
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Abstract

We prove local rigidity of the vanishing Szegő log-term for integral Kähler--Einstein polarizations of a product of irreducible compact Hermitian symmetric spaces. Near the invariant metric, vanishing of the log-term forces the Kähler form to lie in its biholomorphic orbit. The argument combines the first variation of the Kempf distortion function with a central-positioning procedure, reducing rigidity to polynomiality of spectral multipliers of the Laplace operator and the Berezin transform. For integral Kähler--Einstein polarizations, a common-pole obstruction then rules out all infinitesimal deformations transverse to the automorphism orbit.

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Cite

BibTeXRIS
BibTeX
@misc{loi2026szegő,
  title = {{The Szegő log-term and local rigidity of Kähler--Einstein polarizations of compact Hermitian symmetric spaces}},
  author = {Andrea Loi and Matteo Palmieri and Fabio Zuddas},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.12708},
  eprint = {2611.12708},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.12708},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Szegő log-term and local rigidity of Kähler--Einstein polarizations of compact Hermitian symmetric spaces
AU  - Andrea Loi
AU  - Matteo Palmieri
AU  - Fabio Zuddas
PY  - 2026
DA  - 2026/11/09
PB  - arXiv
DO  - 10.48550/arxiv.2611.12708
UR  - https://arxiv.org/abs/2611.12708
AB  - We prove local rigidity of the vanishing Szegő log-term for integral Kähler--Einstein polarizations of a product of irreducible compact Hermitian symmetric spaces. Near the invariant metric, vanishing of the log-term forces the Kähler form to lie in its biholomorphic orbit. The argument combines the first variation of the Kempf distortion function with a central-positioning procedure, reducing rigidity to polynomiality of spectral multipliers of the Laplace operator and the Berezin transform. For integral Kähler--Einstein polarizations, a common-pole obstruction then rules out all infinitesimal deformations transverse to the automorphism orbit.
ER  -