The Zariski cancellation problem for affine space asks whether an affine variety whose product with
an affine line is affine 
-space must be affine 
-space. Over 
, its algebraic formulation asks whether ![A[w]=C[x_1,...,x_(n+1)]](/images/equations/ZariskiCancellationProblem/Inline4.svg)
implies ![A=C[x_1,...,x_n]](/images/equations/ZariskiCancellationProblem/Inline5.svg)
for a finitely
generated complex algebra 
, with scalar-preserving isomorphisms.
Zariski Cancellation Problem
See also
Affine Space, Affine Variety, Coordinate Polynomial, Holomorphic Cancellation Problem, Polynomial Ring, Stable Coordinate ConjectureExplore with Wolfram|Alpha
References
Gupta, N. "The Zariski Cancellation Problem and Related Problems in Affine Algebraic Geometry." In Proc. International Congress of Mathematicians 2022, Vol. 3: Sections 1-4 (Ed. D. Beliaev and S. Smirnov). Berlin, Germany: EMS Press, pp. 1578-1598, 2023. https://doi.org/10.4171/ICM2022/151.Cite this as:
Weisstein, Eric W. "Zariski Cancellation Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ZariskiCancellationProblem.html