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Non-uniruledness and the cancellation problem

Robert Dryło (2005)

Annales Polonici Mathematici

Using the notion of uniruledness we indicate a class of algebraic varieties which have a stronger version of the cancellation property. Moreover, we give an affirmative solution to the stable equivalence problem for non-uniruled hypersurfaces.

Non-uniruledness and the cancellation problem (II)

Robert Dryło (2007)

Annales Polonici Mathematici

We study the following cancellation problem over an algebraically closed field of characteristic zero. Let X, Y be affine varieties such that $X \times^{m} ≅ Y \times^{m}$ for some m. Assume that X is non-uniruled at infinity. Does it follow that X ≅ Y? We prove a result implying the affirmative answer in case X is either unirational or an algebraic line bundle. However, the general answer is negative and we give as a counterexample some affine surfaces.

Number of singular points of an annulus in $ℂ^{2}$

Maciej Borodzik, Henryk Zołądek (2011)

Annales de l’institut Fourier

Using BMY inequality and a Milnor number bound we prove that any algebraic annulus $ℂ^{*}$ in $ℂ^{2}$ with no self-intersections can have at most three cuspidal singularities.

Displaying 1 – 3 of 3

Non-uniruledness and the cancellation problem

Non-uniruledness and the cancellation problem (II)

Number of singular points of an annulus in ℂ 2

Currently displaying 1 – 3 of 3

Number of singular points of an annulus in $ℂ^{2}$