The Chow Ring of a Cubic Hypersurface

The Chow-Witt ring

On the Chow Ring Of

We describe the Chow ring with rational coefficients of the moduli space of stable maps with marked points M0,m(P , d) as the subring of invariants of a ring B(M0,m(P , d);Q), relative to the action of the group of symmetries Sd. B (M0,m(P , d);Q) is computed by following a sequence of intermediate spaces for M0,m(P , d) and relating them to substrata of M0,1(P , d + m − 1). An additive basis f...

The Chow Ring of a Classifying Space

For any linear algebraic group G, we define a ring CHBG, the ring of characteristic classes with values in the Chow ring (that is, the ring of algebraic cycles modulo rational equivalence) for principal G-bundles over smooth algebraic varieties. We show that this coincides with the Chow ring of any quotient variety (V −S)/G in a suitable range of dimensions, where V is a representation of G and...

A Prym Construction for the Cohomology of a Cubic Hypersurface

Mumford defined a natural isomorphism between the intermediate jacobian of a conicbundle over P and the Prym variety of a naturally defined étale double cover of the discrminant curve of the conic-bundle. Clemens and Griffiths used this isomorphism to give a proof of the irrationality of a smooth cubic threefold and Beauville later generalized the isomorphism to intermediate jacobians of odd-di...

The Chow Ring of the Cayley Plane

We give a full description of the Chow ring of the complex Cayley plane OP. For this, we describe explicitely the most interesting of its Schubert varieties and compute their intersection products. Translating our results in the Borel presentation, i.e. in terms of Weyl group invariants, we are able to compute the degree of the variety of reductions Y8 introduced in [6].