arXiv subjects
Publications and source records attributed to Kalyan Banerjee.
In this note we are going to understand two questions. One is the fiber of the natural map from a projective algebraic group $G$ to $G/Γ$, where $Γ$ denotes the $Γ$-equivalence on $G$. The other one is to define a natural map from Hilbert scheme of the generic fiber of a fibration $X\to S$ to the Chow group of relative zero cycles on $X\to S$ and to understand the fibers of this map.
In this article we generalize the injectivity of the push-forward homomorphism at the level of Chow groups, induced by the closed embedding of $\Sym^m C$ into $\Sym^n C$ for $m\leq n$, where $C$ is a smooth projective curve, to symmetric powers of a smooth projective variety of higher dimension. We also prove the analog of this theorem for product of symmetric powers of smooth projective varieties. As an application we prove the injectivity of the push-forward homomorphism at the level of Chow groups, induced by the closed embedding of self product of theta divisor into the self product of the Jacobian of a smooth projective curve.
In this text we are going to discuss the relation between monodromy and algebraic cycles.
In this note we prove that the kernel of the push-forward homomorphism on $d$-cycles modulo rational equivalence, induced by the closed embedding of an ample divisor linearly equivalent to some multiple of the theta divisor inside the Jacobian variety $J(C)$ is trivial. Here $C$ is a smooth projective curve of genus $g$.