Concept

Koras–Russell cubic threefold

Summary
In algebraic geometry, the Koras–Russell cubic threefolds are smooth affine complex threefolds diffeomorphic to \mathbf{C}^3studied by . They have a hyperbolic action of a one-dimensional torus \mathbf{C}^with a unique fixed point, such that the quotients of the threefold and the tangent space of the fixed point by this action are isomorphic. They were discovered in the process of proving the Linearization Conjecture in dimension 3. A linear action of \mathbf{C}^ on the affine space \mathbf{A}^n is one of the form t*(x_1,\ldots,x_n)=(t^{a_1}x_1,t^{a_2}x_2,\ldots,t^{a_n}x_n), where a_1,\ldots,a_n\in \mathbf{Z} and t\in\mathbf{C}^. The Linearization Conjecture in dimension n says that every algebraic action of \mathbf{C}^ on the complex affine space \mathbf{A}^n is linear in some algebraic coordinates on \mathbf{A}^n. M. Koras and P. Rus
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications

No results

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading