Chow Ring of the Moduli Space of Stable Sheaves Supported on Quartic Curves

Abstract

Let M(4, 1) be the moduli space of stable sheaves on P2 with Hilbert polynomial 4m + 1. Then A∗(M(4, 1),Q) ∼= Q[α, β, x , y , z ]/〈xz − yz , β2z − 3yz − 9z2, 3α2z − αβz + yz , β2y − 3y 2 − 9yz , β2x − xy − 3y 2 − 3αβz − 9yz + 9z2, β4 + 3x 2 − 9xy − 3y 2 − 54yz − 81z2, βyz + 9αz2 − 3βz2, 2βxy − 3βy 2− 9αyz − 27αz2 + 9βz2, 3βx 2− 7βy 2− 36αyz − 108αz2 + 36βz2, α12 + 3α11β + 3α10(β2 + 2x − y) + α9(−β3 + 12βx + 2βy) +3α8(9x 2 − 16xy + 27y 2) + 28α7βy 2 + 56α6y 3 + 201αβz5 − 19yz5 − 613z6, 6α10xy − 12α10y 2 − 10α9βy 2 − 45α8y 3 − 104αβz6 + 2yz6 + 310z7〉 where α, β are of degree 1 and x , y , z are of degree 2. Idea of Proof