October 16, 2025Open Access

Complexes of differential forms and singularities: The injectivity theorem

Key Points

The natural morphism from the Grothendieck dual is injective on cohomology.
This result pertains to varieties with (m-1)-Du Bois singularities, confirming a long-standing conjecture.
The work proves a significant result in algebraic geometry concerning dual complexes and singularities.
The injectivity theorem establishes a key linkage between Du Bois singularities and cohomological properties.

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.

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Cite This Study

Sándor J. Kovács (Thu,) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd21c https://doi.org/https://doi.org/10.48550/arxiv.2505.09912

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