Year: 2024
Type: article
Abstract: For each classical irreducible bounded symmetric domain $$\mathcal {D}$$ D , Klingler has computed the minimum number $$m_{\mathcal {D}}$$ m D such that any smooth projective quotient $$X=\mathcal {D}/\Gamma $$ X = D / Γ , for $$\Gamma \in \text {Aut}^0(\mathcal {D})$$ Γ ∈ Aut 0 ( D ) , satisfies $$H^0(X,\textrm{Sym}^i\Omega ^1_X)=0$$ H 0 ( X , Sym i Ω X 1 ) = 0 for $$0 0 < i < m D . In this article, we extend Klingler’s result to the case when X is normal and projective. This, together with a normal version of Arapura’s result about the relationship between the vanishing of global symmetric differentials on X and the rigidity of finite dimensional representations of $$\pi _1(X)$$ π 1 ( X ) , gives rigidity statements for representations of $$\pi _1(X)$$ π 1 ( X ) and $$\pi _1(X_{reg})$$ π 1 ( X reg ) in a low dimensional range, when X is a normal projective quotient of a bounded symmetric domain.
Source: Geometriae Dedicata
Author: Aryaman Patel
Institution: Saarland University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
OpenAlex ID: W4404779627