5 papers
Lower bounds for the Smith-Thom deficiency of Hilbert squares
Viatcheslav Kharlamov, Rareş Răsdeaconu
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 pro…
On maximality of involutions of hyper-Kähler manifolds and punctual Hilbert schemes of surfaces
Simone Billi, Lie Fu, Annalisa Grossi +1
Given a holomorphic or anti-holomorphic involution on a complex variety, the Smith inequality says that the total -Betti number of the fixed locus is no greater than…
On the Smith-Thom deficiency of Hilbert squares
Viatcheslav Kharlamov, Rareş Răsdeaconu
We give an expression for the Smith-Thom deficiency of the Hilbert square of a smooth real algebraic variety in terms of the rank of a suitable Mayer-Vietoris mapping…
Unexpected loss of maximality: the case of Hilbert square of real surfaces
Viatcheslav Kharlamov, Rareş Răsdeaconu
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 lo…
Diffeomorphisms, Isotopoies, and Braid Monodromy Factorizations of Plane Cuspidal Curves
V. Kharlamov, Vik. S. Kulikov
We prove that there is an infinite sequence of pairs of plane cuspidal curves and , such that the pairs and are dif…