Complexes of differential forms and singularities: The injectivity theorem
arXiv:2505.09912
Abstract
In this paper, it is proved, that for varieties with (m-1)-Du Bois singularities, the natural morphism from the Grothendieck dual of the m-th graded Du Bois complex to the Grothendieck dual of its zero-th cohomology sheaf is injective on cohomology. This confirms Conjecture G of Popa, Shen, and Vo [PSV24].
v2: Added Cor. 10.11 and Cor. 10.12 v3: Added Prop 2.3 and simplified proof of the main theorem v4: corrected several typos, simplified proof in "proper-to-local" section. Number of pages reduced significantly. v5: Fixed an issue with a local cohomology argument, further reduced length