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PreprintarXiv licencearXiv

Perverse Euler Characteristics of Hermitian Locally Symmetric Spaces

  • Mert Akdenizli
  • Quoc-Anh Tran
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Abstract

We prove that finite-volume locally Hermitian symmetric spaces of noncompact type have nonnegative perverse Euler characteristics. To show this, we obtain a nefness result for the logarithmic cotangent bundle of a smooth toroidal compactification. Combining this with a positivity criterion for Euler characteristics of perverse sheaves, we deduce the nonnegativity result. We further prove that the inequality is strict for perverse sheaves with full support. As applications, we get nonnegativity results for perverse Euler characteristics on various moduli spaces.

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Cite

BibTeXRIS
BibTeX
@misc{akdenizli2026perverse,
  title = {{Perverse Euler Characteristics of Hermitian Locally Symmetric Spaces}},
  author = {Mert Akdenizli and Quoc-Anh Tran},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10946},
  eprint = {2609.10946},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10946},
}
RIS
TY  - UNPB
TI  - Perverse Euler Characteristics of Hermitian Locally Symmetric Spaces
AU  - Mert Akdenizli
AU  - Quoc-Anh Tran
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.10946
UR  - https://arxiv.org/abs/2609.10946
AB  - We prove that finite-volume locally Hermitian symmetric spaces of noncompact type have nonnegative perverse Euler characteristics. To show this, we obtain a nefness result for the logarithmic cotangent bundle of a smooth toroidal compactification. Combining this with a positivity criterion for Euler characteristics of perverse sheaves, we deduce the nonnegativity result. We further prove that the inequality is strict for perverse sheaves with full support. As applications, we get nonnegativity results for perverse Euler characteristics on various moduli spaces.
ER  -