On a result of Green and Griffiths
Qizheng Yin
TL;DR
This paper provides an elementary proof that a specific 0-cycle related to generic curves of genus at least 4 is non-torsion in the Chow group, applicable across all characteristics.
Contribution
It offers a simple, characteristic-independent proof of Green and Griffiths' result on the non-torsion of a certain 0-cycle for generic curves.
Findings
The 0-cycle K × K - (2g - 2) K_Δ is non-torsion in CH^2(C × C).
The proof is elementary and works in all characteristics.
Confirms Green and Griffiths' result with a simpler approach.
Abstract
We present a simple proof of a result of Green and Griffiths, which states that for the generic curve C of genus g >= 4, the 0-cycle K \times K - (2g - 2) K_\Delta is non-torsion in CH^2(C \times C). The proof is elementary and works in all characteristics.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Analytic Number Theory Research