Boundary branch divisor of toroidal compactifications

TL;DR

This paper proves that toroidal compactifications of certain arithmetic quotients of Hermitian symmetric domains do not have boundary branch divisors when the algebraic group is of adjoint type.

Contribution

It establishes a new result showing the absence of boundary branch divisors in these compactifications under specific algebraic conditions.

Findings

No boundary branch divisor in the compactifications.

Applicable to algebraic groups of adjoint type.

Advances understanding of boundary behavior in Hermitian symmetric domain compactifications.

Abstract

We prove that any toroidal compactification of arithmetic quotient of Hermitian symmetric domain has no boundary branch divisor, in the setting where the algebraic group is of adjoint type.