Betti numbers of GIT quotients of products of projective planes

2009/03/30 by Incensi, Francesca
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0903.5235

Abstract

We study the GIT quotients for the diagonal action of the algebraic group SL₃(ℂ) on the n-fold product of ℙ²(ℂ): in particular we determine a strategy in order to determine the (intersection) Poincaré polynomial of any quotient variety. In the special case n=6 we determine an explicit formula for the (intersection) Betti numbers of a quotient variety, depending only on the combinatorics of the weights of the polarization m∈ ℤ⁶_>0.

Related

• GIT quotients of products of projective spaces
• The Betti Numbers of a Determinantal Variety
• Bounds on the individual Betti numbers of complex varieties, stability and algorithms
• Intersection Poincare polynomial for Nagaraj-Seshadri moduli space
• GIT stability of divisors in products of projective spaces