Gross–Schoen cycles and dualising sheaves
By Shou-wu Zhang. 2008
122 citations recorded by the source corpus.
The aim of this paper is to study the modified diagonal cycle in the triple product of a curve over a global field defined by Gross and Schoen. Our main result is an identity between the height of this cycle and the self-intersection of the relative dualising sheaf. We have some applications to the following problems in number theory and algebraic geometry.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/720b19e8b7581fc60b2a29f09b141ba96226644a
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Zhang’s Conjecture and the Effective Bogomolov Conjecture over function fields (2009, methodology): “Replacing the function field K by a finite extension, we may assume that there is a divisor ξ of degree 1 on C such that (2 ¯ g − 2)ξ is rationally equivalent to the canonical divisor KC .L et� ξ be the canonical Gross-Schoen cycle associated to X. Further information about � ξ can be found in the a”