From the 1 of 7 linked papers with an AI index.
7 papers · 1 filter
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…
Hodge symmetry and Lefschetz theorems for singular varieties
Sung Gi Park, Mihnea Popa
We prove new results concerning the topology and Hodge theory of singular varieties. A common theme is that concrete conditions on the complexity of the singularities, from a numbe…
Q-factoriality and Hodge-Du Bois theory
Sung Gi Park, Mihnea Popa
We prove Hodge-theoretic formulas for the -factoriality defect of a normal projective variety, and for the local analytic -factoriality defect of an analyti…
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.
On the behavior of Kodaira dimension under smooth morphisms
Mihnea Popa, Christian Schnell
We prove several results on the additivity of Kodaira dimension under smooth morphisms of smooth projective varieties.