arXiv subjects
Publications and source records attributed to Sándor Kovács.
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].
A partial answer is given to a question raised by Kovács and Taji in arxiv:2307.07192, namely that the relative Du Bois complex of a family parametrized by a non-singular curve commutes with base change to a general point on the base. It is also shown that this property usually fails for special points.
This work establishes simple criteria for detecting higher rational singularities via the intersection Du Bois complex and the irrationality complex of a normal variety over the complex numbers.