Related papers: Algebraic cycles on Jacobian varieties

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…

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…

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 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 show that on the Jacobian $(JC,\theta)$ of a smooth curve $C$ of genus $g$, any effective cycle in $JC$ with cohomology class $\theta^d/d!$ is a translate of $W_{g-d}(C)$ or $-W_{g-d}(C)$. We then use this result to prove that for…

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…

We study tautological cycle classes on the Jacobian of a curve. We prove a new result about the ring of tautological classes on a general curve that allows, among other things, easy dimension calculations and leads to some general results…

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…

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…

In this paper, we consider the tautological ring containing the extended Brill-Noether algebraic classes on the normalization of the compactified Jacobian of a complex nodal projective curve (with one node). This smallest $\Q$-subalgebra of…

We prove the integral Hodge conjecture for one-cycles on a principally polarized complex abelian variety whose minimal class is algebraic. In particular, any product of Jacobians of smooth projective curves over the complex numbers…

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…

Let $\MC$ be the moduli space of stable holomorphic vector bundles of rank 2 and fixed determinant of odd degree, over a smooth projective curve $C$. This paper identifies the algebraic cohomology ring $\HA^*(\MC)$, i.e. the subring of the…

Klein's simple group $H$ of order $168$ is the automorphism group of the plane quartic curve $C$, called Klein quartic. By Torelli Theorem, the full automorphism group $G$ of the Jacobian $J=J(C)$ is the group of order $336$, obtained by…

We consider the moduli space $\cSU_C^s(r,\cO_C)$ of rank r stable vector bundles with trivial determinant on a smooth projective curve $C$ of genus $g$. We show that the Abel-Jacobi map on the rational Chow group…

This thesis intends to make a contribution to the theories of algebraic cycles and moduli spaces over the real numbers. In the study of the subvarieties of a projective algebraic variety, smooth over the field of real numbers, the cycle…

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…

We consider two cycles on the moduli space of compact type curves and prove that they coincide. The first is defined by pushing forward the virtual fundamental classes of spaces of relative stable maps to an unparameterized rational curve,…

Algebraic cycles on complex projective space P(V) are known to have beautiful and surprising properties. Therefore, when V carries a real or quaternionic structure, it is natural to ask for the properties of the groups of real or…

In this paper, we consider the moduli space $\cSU_C(r,\cO_C)$ of rank $r$ semistable vector bundles with trivial determinant on a smooth projective curve $C$ of genus $g$. When the rank $r=2$, F. Kirwan constructed a smooth log resolution…