From the 1 of 4 linked papers with an AI index.
4 papers
Negative -theory and Hodge theory
Andrew Burke, Mihnea Popa, Wanchun Shen
The paper investigates negative K‑groups of complex algebraic varieties using mixed Hodge theory, incorporating tools such as higher singularities, Chow groups, and the Minimal Mod…
On higher Du Bois singularities and -regularity
Wanchun Shen
We study the relationship between higher Du Bois singularities and -regularity, a notion that measures the -invariance of the algebraic -groups. Building on thi…
Elimination Templates in Macaulay2
Manav Batavia, Cheng Chen, Anna Natalie Chlopecki +4
We introduce the package \texttt{EliminationTemplates} for the Macaulay2 computer algebra system, which provides tools for constructing automatic solvers for families of zero-dimen…
Injectivity and Vanishing for the Du Bois Complexes of Isolated Singularities
Mihnea Popa, Wanchun Shen, Anh Duc Vo
We prove an injectivity theorem for the cohomology of the Du Bois complexes of varieties with isolated singularities. We use this to deduce vanishing statements for the cohomologie…