Some results on the codimension-two Chow group of the moduli space of stable curves. (English) Zbl 0696.14004
Algebraic curves and projective geometry, Proc. Conf., Trento/Italy 1988, Lect. Notes Math. 1389, 66-75 (1989).
[For the entire collection see Zbl 0667.00008.]
The author studies the Chow group \(A^ 2(\bar M_ g)\) of codimension- two cycles of the moduli space \(\bar M_ g\) of stable curves of genus g over \({\mathbb{C}}\). More precisely: \((1)\quad He\) describes generators for the subspace of \(A^ 2(\bar M_ g)\) of cycles coming from the boundary \(\bar M_ g-M_ g\); (2) for \(g=3\) and \(g=5\) he shows that in \(A^ 2(\bar M_ g)\) the products of the divisor classes in a basis of \(A^ 1(\bar M_ g)\) are linearly independent; and (3) for \(g=3\) he gives a description of the ring \(A^*(\bar M_ 3)\) while for \(g=4\) he proves that the dimension of \(A^ 2(\bar M_ 4)\) is 13.
The author studies the Chow group \(A^ 2(\bar M_ g)\) of codimension- two cycles of the moduli space \(\bar M_ g\) of stable curves of genus g over \({\mathbb{C}}\). More precisely: \((1)\quad He\) describes generators for the subspace of \(A^ 2(\bar M_ g)\) of cycles coming from the boundary \(\bar M_ g-M_ g\); (2) for \(g=3\) and \(g=5\) he shows that in \(A^ 2(\bar M_ g)\) the products of the divisor classes in a basis of \(A^ 1(\bar M_ g)\) are linearly independent; and (3) for \(g=3\) he gives a description of the ring \(A^*(\bar M_ 3)\) while for \(g=4\) he proves that the dimension of \(A^ 2(\bar M_ 4)\) is 13.
Reviewer: A.Papantonopoulou
