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

2023/03/05 by Viatcheslav Kharlamov, Kharlamov, Viatcheslav, Rareş Răsdeaconu +1
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2303.02796

Abstract

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.

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