5 papers
Negative -theory and Hodge theory
Andrew Burke, Mihnea Popa, Wanchun Shen
We study the negative -groups of complex varieties from a mixed Hodge-theoretic perspective, making use of the theory of higher singularities, Chow groups, and the Minimal Model…
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…
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…
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…
Du Bois complexes of cones over singular varieties, local cohomological dimension, and K-groups
Mihnea Popa, Wanchun Shen
We compute the Du Bois complexes of abstract cones over singular varieties, and use this to describe the local cohomological dimension and the non-positive K-groups of such cones.