2025/09/01 by L Fehér, Fehér, László M., András P. Juhász +1
Mathematics · #05A15 #05A16 #11B73 #14N10 #55N91 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2509.01725
openalex publication_date 2025/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the d-dependence of c(Pold(ℂn)), the Chern class of the GL(n)-representation of degree d homogeneous polynomials in n complex variables is polynomial. We also study the asymptotics of the polynomial d-dependence of this Chern class. We apply these results to solve a conjecture of Manivel on the degree of varieties of hypersurfaces containing linear subspaces. We also prove new formulas for the degree and Euler characteristics of Fano schemes of lines for generic hypersurfaces. To prove the polynomial dependence of c(Pold(ℂn)) we introduce the notion of Striling coefficients. This can be considered as a generalization of Stirling numbers. We express the Stirling coefficients in terms of specializations of monomial symmetric polynomials so we can deduce their polynomiality and, in certain cases, their asymptotic behaviour.