Jongbaek Song, Regular Hessenberg Varieties and Toric Varieties

A Hessenberg variety is a subvariety of the flag variety (G/B) determined by two parameters: one is an element of the Lie algebra of G and the other is a B-submodule containing the Lie algebra of B, known as a Hessenberg space. In this talk, we focus on elements in the regular locus of the Lie algebra and the Hessenberg space determined by negative simple roots. Then, we aim to figure out cohomological relationship of these Hessenberg varieties with a certain class of toric varieties having orbifold singularities. The main result raises an interesting topic concerning toric varieties with symmetries by reflections. This is a joint work with M. Masuda, T. Horiguchi and J. Shareshian.