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Motivated by the computation of the BPS-invariants on a local Calabi-Yauthreefold suggested by S. Katz, we compute the Chow ring and the cohomologyring of the moduli space of stable sheaves of Hilbert polynomial $4m+1$ on theprojective plane. As a byproduct, we obtain the total Chern class and Eulercharacteristics of all line bundles, which provide a numerical data for thestrange duality on the plane.

Chow ring of the moduli space of stable sheaves supported on quartic curves