arXiv subjects

Rareş Răsdeaconu

Publications and source records attributed to Rareş Răsdeaconu.

4 recordsLinked to original sources

arXiv2026

Lower bounds for the Smith-Thom deficiency of Hilbert squares

We establish lower bounds for the Smith--Thom deficiency of the Hilbert square of a maximal nonsingular real projective variety. These bounds recover the known surface case and provide new obstructions to Smith-Thom maximality in every dimension at least two. As applications, we prove that the Hilbert square of any real abelian variety of dimension at least two is not Smith-Thom maximal. We further show that the deficiencies of the Hilbert squares of maximal real abelian varieties grow exponentially with the dimension. We also obtain nonmaximality results for the Hilbert squares of certain Cartesian products.

math.AG↗

arXiv2026

Kalinin Effectivity and Wonderful Compactifications

We review the definition and main properties of Kalinin effectivity and describe methods for constructing effective spaces together with several examples. We analyze the Kalinin effectivity of wonderful compactifications and prove that the wonderful compactifications of hyperplane arrangements and of configuration spaces associated to Kalinin effective compact complex manifolds are themselves Kalinin effective. As an application, we show that the Deligne-Mumford space of real rational curves with marked points is effective. Finally, we apply Kalinin effectivity to study Smith-Thom maximality for Hilbert squares.

math.AG↗

arXiv2025

Unexpected loss of maximality: the case of Hilbert square of real surfaces

We explore the maximality of the Hilbert square of maximal real surfaces, and find that in many cases the Hilbert square is maximal if and only if the surface has connected real locus. In particular, the Hilbert square of no maximal K3-surface is maximal. Nevertheless, we exhibit maximal surfaces with disconnected real locus whose Hilbert square is maximal.

math.AG↗

arXiv2025

On the Smith-Thom deficiency of Hilbert squares

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.

math.AG↗