A Remark on a Paper of Crachiola and Makar-Limanov

• Autorzy: Dryło R.

Identyfikatory

DOI

10.4064/ba59-3-2

• Języki publikacji: EN

Abstrakty

EN

A. Crachiola and L. Makar-Limanov [J. Algebra 284 (2005)] showed the following: if X is an affine curve which is not isomorphic to the affine line A1k, then ML(X×Y)=k[X]⊗ML(Y) for every affine variety Y, where k is an algebraically closed field. In this note we give a simple geometric proof of a more general fact that this property holds for every affine variety X whose set of regular points is not k-uniruled.

Słowa kluczowe

EN

Makar-Limanov invariant; additive group actions; cancellation problem

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: Vol. 59, no 3
• Strony: 203--206
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Dryło R.

• Instytut Matematyczny PAN Śniadeckich 8 00-956 Warszawa, Poland
• Instytut Matematyki Uniwersytet Jana Kochanowskiego w Kielcach Świętokrzyska 15 25-406 Kielce, Poland [e-mail]

Bibliografia

• [1] S. S. Abhyankar, P. Eakin and W. Heinzer, On the uniqueness of the coefficient ring in a polynomial ring, J. Algebra 23 (1972), 310–342.
• [2] A. Crachiola and L. Makar-Limanov, On the rigidity of small domains, ibid. 284 (2005), 1–12.
• [3] R. Dryło, Non-unirulednees and the cancellation problem (II), Ann. Polon. Math. 92 (2007), 41–48.
• [4] T. Fujita and S. Iitaka, Cancellation theorem for algebraic varieties, J. Fac. Sci. Univ. Tokyo 24 (1977), 123–127.
• [5] S. Iitaka, An Introduction to Birational Geometry of Algebraic Varieties, Springer, New York, 1982.
• [6] Z. Jelonek, Testing sets for properness of polynomial mappings, Math. Ann. 315 (1999), 1–35.
• [7] A. Stasica, Geometry of the Jelonek set, J. Pure Appl. Algebra 137 (2005), 49–55.