The variation of the Gysin kernel in a family
Abstract
Consider a smooth projective surface $S$. Consider a fibration $S\to C$ 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 $\{j_{t*}\}_{t\in C}$ from the Jacobian $J(C_t)$ to $A_0(S)$ 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 $\mathscr{J}\to C$, such that the fiber of this countable union at $t$ is the kernel of $j_{t*}$.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.02116
- arXiv:
- arXiv:1806.02116
- Bibcode:
- 2018arXiv180602116B
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14C25
- E-Print:
- 8 pages