On the Smith-Thom deficiency of Hilbert squares

Viatcheslav Kharlamov; Rareş Răsdeaconu

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arXiv · 2310.19120

On the Smith-Thom deficiency of Hilbert squares

Viatcheslav Kharlamov·Rareş Răsdeaconu

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Abstract

We give an expression for the Smith-Thom deficiency of the Hilbert square $X^{[2]}$ of a smooth real algebraic variety $X$ in terms of the rank of a suitable Mayer-Vietoris mapping in several situations. As a consequence, we establish a necessary and sufficient condition for the maximality of $X^{[2]}$ in the case of projective complete intersections, and show that with a few exceptions no real nonsingular projective complete intersection of even dimension has maximal Hilbert square. We also provide new examples of smooth real algebraic varieties with maximal Hilbert square.

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BibTeX RIS

Viatcheslav Kharlamov, Rareş Răsdeaconu. 2025-04-12. On the Smith-Thom deficiency of Hilbert squares. https://arxiv.org/abs/2310.19120

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