Cycle connectivity and pseudoconcavity of flag domains

TL;DR

This paper investigates the geometric properties of non-classical flag domains and period domains, establishing conditions under which they are pseudoconcave, with implications for their boundary structures and Hodge theory.

Contribution

It provides new criteria for pseudoconcavity in non-classical flag and period domains based on root systems and Hodge-theoretical conditions.

Findings

Non-classical flag domains are pseudoconcave under specific root system conditions.

Boundary points in certain period domains are pseudoconcave if they meet Hodge-theoretical criteria.

The results connect geometric properties with algebraic and Hodge-theoretic structures.

Abstract

We prove that a non-classical flag domain is pseudoconcave if it satisfies a certain condition on the root system. Moreover, we prove that every point in a one-codimensional real boundary orbit of a non-classical period domains is a pseudoconcave boundary point if it satisfies a certain Hodge-theoretical condition.