Cohomological χ-dependence of ring structure for the moduli of one-dimensional sheaves on ℙ²

2023/05/23 by Woonam Lim, Lim, Woonam, Miguel Moreira +3
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2305.14193

openalex publication_date 2023/05/23 · openalex created_date 2023/05/27 · openalex updated_date 2026/07/28

Abstract

We prove that the cohomology rings of the moduli space M_d,χ 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 χ-independence of the Betti numbers of these moduli spaces. As a corollary, we deduce that M_d,χ are topologically different unless they are related by obvious symmetries, strengthening a previous result of Woolf distinguishing them as algebraic varieties.

Related

• Some Betti numbers of the moduli of 1-dimensional sheaves on ℙ²
• Cohomology rings of the moduli of one-dimensional sheaves on the projective plane
• Generators for the cohomology ring of the moduli of one-dimensional sheaves on ℙ²
• Motivic measures of the moduli spaces of pure sheaves on ℙ² with all degrees
• On the perverse filtration of the moduli spaces of 1-dimensional sheaves on ℙ² and P=C conjecture