2023/10/29 by Viatcheslav Kharlamov, Kharlamov, Viatcheslav, Rareş Răsdeaconu +1
Computer Science · Mathematics · #14C05 #14J99 #14P25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric Topology (math.GT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2310.19120
openalex publication_date 2023/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.