5 papers · 1 filter
Intrinsic Restriction Traces and Toric Dynamics
Haoyang Liu, Tianle Liu
We prove Morita invariance of the Campbell--Lind--Malkiewich--Ponto--Zakharevich restriction-system trace after passage to perfect modules. It therefore defines an intrinsic integr…
Two-flag degenerations and real circles tangent to three conics
Haoyang Liu, Tianle Liu, Guorui Xu +1
Three general plane conics admit complex tangent circles, and it had been conjectured that at most of them could be real. We construct an explicit strongly general trip…
A Fan Algorithm for Chow-Witt Rings of Smooth Projective Toric Varieties
Haoyang Liu, Tianle Liu, Guorui Xu
Let be a real closed field and let be a smooth projective split toric variety. For an explicitly chosen basis rigidification of its Picard grading, we prove…
Torus-enriched Motivic Bruhat Complexes and Maximal Compact Groups
Haoyang Liu, Tianle Liu
Bruhat decompositions give cellular models for split algebraic groups, flag varieties, and maximal compact groups, but motivic boundaries retain orientation and torus-translation d…
Cellular -Homology from Bruhat Boundary Matrices of Split Semisimple Flag Varieties
Haoyang Liu, Tianle Liu
Let be a perfect field of characteristic different from 2, we compute the cellular -homology of the flag varieties attached to split semisimple simply con…