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Division theorems for the rational cohomology of some discriminant complements

Alexei G. Gorinov
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Abstract

The main purpose of this paper is to show that the mixed Hodge polynomial of the ``space of equations'' for smooth complete intersections of given multidegree in $\mathbb{C} P^n$ is divisible by the mixed Hodge polynomial of the group $\mathrm{GL}_{n+1}(\mathbb{C})$, the quotient being the mixed Hodge polynomial of the corresponding quotient space. As a by-product of the method used in the proof, we obtain expressions divisible by the order the automorphism group of any smooth projective hypersurface of given dimension and degree

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Alexei G. Gorinov. 2005-11-23. Division theorems for the rational cohomology of some discriminant complements. https://arxiv.org/abs/math/0511593

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