Related papers: Relations between tautological cycles on Jacobians

We consider the Chow ring with rational coefficients of the Jacobian of a curve. Assume D is a divisor in a base point free g^r_d of the curve such that the canonical divisor K is a multiple of the divisor D. We find relations between…

Let C be a curve over a non-singular base variety S. We study algebraic cycles on the symmetric powers C^[n] and on the Jacobian J. The Chow homology of C^[*], the sum of all C^[n], is a ring using the Pontryagin product. We prove that this…

We present a collection of algebraic equivalences between tautological cycles on the Jacobian $J$ of a curve, i.e., cycles in the subring of the Chow ring of $J$ generated by the classes of certain standard subvarieties of $J$. These…

By using the Grothendieck-Riemann-Roch theorem we derive cycle relations modulo algebraic equivalence in the Jacobian of a curve. The relations generalize the relations found by Colombo and van Geemen and are analogous to but simpler than…

We present relations between cycles with rational coefficients modulo algebraic equivalence on the Jacobian of a curve. These relations depend on the linear systems the curve admits. They are obtained in the tautological ring, the smallest…

We connect two notions of tautological ring: one for the moduli space of curves (after Mumford, Faber, etc.), and the other for the Jacobian of a curve (after Beauville, Polishchuk, etc.). The motivic Lefschetz decomposition on the Jacobian…

In this paper we construct and study the actions of certain deformations of the Lie algebra of Hamiltonians on the plane on the Chow groups (resp., cohomology) of the relative symmetric powers ${\cal C}^{[\bullet]}$ and the relative…

We study tautological classes on the moduli space of stable $n$-pointed hyperelliptic curves of genus $g$ with rational tails. Our result gives a complete description of tautological relations. The method is based on the approach of Yin in…

For a family of Jacobians of smooth pointed curves there is a notion of tautological algebra. There is an action of $\mathfrak{sl}_2$ on this algebra. We define and study a lifting of the Polishchuk operator, corresponding to $f\in…

For a curve C, viewed as a cycle in its Jacobian, we study its image n_*C under multiplication by n on JC. We prove that the subgroup generated by these cycles, in the Chow group modulo algebraic equivalence, has rank at most d-1, where d…

Let $J$ be the Jacobian of a smooth projective complex curve $C$ which admits non-trivial automorphisms, and let $A(J)$ be the ring of algebraic cycles on $J$ with rational coefficients modulo algebraic equivalence. We present new…

Let C be a complex curve of genus g, let J(C) be its Jacobian and let R(C) be its tautological ring, that is, the group of algebraic cycles modulo algebraic equivalence. We study the algebraic structure of R(C). In particular, we give a…

We present a conjecture for the Chow ring of the universal moduli stack of bundles over hyperelliptic curves and prove it for rank and genus two. Consequently, we obtain explicit generators and relations to conclude that the Chow ring is…

Let $J$ be the Jacobian of a smooth projective curve. We define a natural action of the Lie algebra of polynomial Hamiltonian vector fields on the plane, vanishing at the origin, on the Chow group of $J$ with rational coefficients. Using…

The classical Poincar\'e formula relates the rational homology classes of tautological cycles on a Jacobian to powers of the class of Riemann theta divisor. We prove a tropical analogue of this formula. Along the way, we prove several…

Let J be the Jacobian of a smooth curve C of genus g, and let A(J) be the ring of algebraic cycles modulo algebraic equivalence on J, tensored with Q. We study in this paper the smallest Q-vector subspace R of A(J) which contains C and is…

Gromov-Witten (GW) theory produces Chow and cohomology classes on the moduli of curves, and there are several conjectures/speculations about their relation to the tautological ring. We develop new degeneration techniques to address these.…

We prove some cycle relations on moduli of K3 surfaces

Let $\bar{X}$ be a smooth quasi-projective $d$-dimensional variety over a field $k$ and let $D$ be an effective Cartier divisor on it. In this note, we construct cycle class maps from (a variant of) the higher Chow group with modulus of the…

The virtual geometry of the moduli space of stable quotients is used to obtain Chow relations among the kappa classes on the moduli space of nonsingular genus g curves. In a series of steps, the stable quotient relations are rewritten in…