Cohomological χ -dependence of ring structure for the moduli of one-dimensional sheaves on P<SUP>2</SUP>

Abstract

We prove that the cohomology rings of the moduli space of one-dimensional sheaves on the projective plane are not isomorphic for general different choices of the Euler characteristics. This stands in contrast to the-independence of the Betti numbers of these moduli spaces. As a corollary, we deduce that are topologically different unless they are related by obvious symmetries, strengthening a previous result of Woolf distinguishing them as algebraic varieties.