Smooth subvarieties of Jacobians
Olivier Benoist, Olivier Debarre
TL;DR
This paper presents new examples of cohomology classes on smooth projective varieties, specifically on Jacobians of very general curves, that cannot be expressed as linear combinations of classes of smooth subvarieties, using complex cobordism.
Contribution
It introduces the first known examples of such classes in dimension 6, employing complex cobordism as the main analytical tool.
Findings
Existence of cohomology classes not generated by smooth subvarieties.
Examples in dimension 6, the minimal possible dimension.
Application of complex cobordism to algebraic geometry.
Abstract
We give new examples of algebraic integral cohomology classes on smooth projective complex varieties that are not integral linear combinations of classes of smooth subvarieties. Some of our examples have dimension 6, the lowest possible. The classes that we consider are minimal cohomology classes on Jacobians of very general curves. Our main tool is complex cobordism.
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