Let X be a smooth complete irreducible curve of genus g over an algebraically closed field, let J be its Jacobian variety, and let X(n) be its n-fold symmetric product. In this very readable article, the author determines the structure of the Chow ring A(X(n)) as an A(J)-algebra. It is the cyclic A(J)-module A(J)[Z]/In, where the ideal In is explicitly described.
The rational equivalence ring of symmetric products of curves. Illinois J. Math. 19 (1975), no. 4, 567--583.
COLLINO, Alberto
1975-01-01
Abstract
Let X be a smooth complete irreducible curve of genus g over an algebraically closed field, let J be its Jacobian variety, and let X(n) be its n-fold symmetric product. In this very readable article, the author determines the structure of the Chow ring A(X(n)) as an A(J)-algebra. It is the cyclic A(J)-module A(J)[Z]/In, where the ideal In is explicitly described.
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