ON THE CHOW RING OF CERTAIN LEHN–LEHN–SORGER–VAN STRATEN EIGHTFOLDS

On the Chow ring of certain algebraic hyper-Kähler manifolds

He proved in [3] this conjecture in the case of the second and third punctual Hilbert scheme of an algebraic K3 surface. In this paper, we observe that the results of [5] can lead to a more general conjecture concerning the Chow ring of an algebraic hyper-Kähler variety. Namely, the full statement of Theorem 0.1 can be interpreted by saying that any polynomial relation between [c2(TS)], [c1(Li)...

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...

On the Chow Ring of M 0

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-Witt ring

On the Chow Groups of Certain Geometrically Rational 5-folds

We give an explicit regular model for the quadric fibration studied in [9]. As an application we show that this construction furnishes a counterexample for the integral Tate conjecture in any odd characteristic for some sufficiently large finite field. We study the étale cohomology of this regular model, and as a consequence we derive that these counterexamples are not torsion.