The variation of the Gysin kernel in a family

2018/06/06 by Kalyan Banerjee, Banerjee, Kalyan
Physics and Astronomy · #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.1806.02116

Abstract

Consider a smooth projective surface S. Consider a fibration S→ C where C is a quasi-projective curve such the fibers are smooth projective curves. The aim of this text is to show that the kernels of the push-forward homomorphism \j_t*\_{t∈ C} from the Jacobian J(C_t) to A₀(S) forms a family in the sense that it is a countable union of translates of an abelian scheme over C sitting inside the Jacobian scheme \mathscrJ→ C, such that the fiber of this countable union at t is the kernel of j_t*.

Related

• The kernel of the Gysin homomorphism for smooth projective curves
• The Kernel of the Gysin homomorphism for positive characteristic
• On the kernel of the push-forward homomorphism between Chow groups
• Kernels of numerical pushforwards
• Non-simple abelian varieties in a family: arithmetic approaches