Exotic embeddings of open subsets of affine space
Author:
Zbigniew Jelonek
Journal:
Proc. Amer. Math. Soc. 140 (2012), 1561-1568
MSC (2010):
Primary 14R10
Posted:
September 12, 2011
MathSciNet review:
2869140
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Abstract: We show that every Zariski open affine proper subset
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Bibliography
1. Abhyankar, S., On the valuations centered in a local domain, Amer. J. Math. 78 , 321-348 (1956). MR 0082477 (18:556b)
2. Abhyankar, S., Moh, T., Embeddings of the line in the plane, J reine angew. Math. 276 , 148-166 (1975). MR 0379502 (52:407)
3. Derksen, H., Kutzsechebauch, F., Winkelmann, J., Subvarieties of J. Reine Angew. Math. 508 , 213-235 (1999). MR 1676877 (2000c:32072)
4. Jelonek, Z., The extension of regular and rational embeddings, Math. Ann. 277 , 113-120 (1987). MR 884649 (88e:14016)
5. Jelonek, Z., Identity sets for polynomial automorphisms, Journal of Pure & Applied Algebra 76 , 333-337 (1991). MR 1147306 (93c:14018)
6. Jelonek, Z., Irreducible identity sets for polynomial automorphisms, Math. Z. 212 , 601-617 (1993). MR 1214049 (94c:14014)
7. Jelonek, Z., A note about the extension of polynomial embeddings, Bull. Acad. Polon. Sci. Math. 43 , 239-244 (1995). MR 1415002 (97i:14011)
8. Jelonek, Z., A hypersurface which has the Abhyankar-Moh property, Math. Ann. 308 , 73-84 (1997). MR 1446200 (98d:14019)
9. Jelonek, Z., Exotic embeddings of smooth affine varieties, Journal of Algebra 297 , 530-541 (2006). MR 2209273 (2006m:14084)
10. Jelonek, Z., Manifolds with a unique embedding, Colloq. Math . 117 , 299-317 (2009). MR 2550135 (2010m:58003)
11. Kaliman, S., Extensions of isomorphisms between affine algebraic subvarieties of Proc. Amer. Math. Soc. 113 , 325-334 (1991). MR 1076575 (91m:14019)
12. Kaliman, S., Zaidenberg, M., Affine modifications and affine hypersurfaces with a very transitive automorphism group, Transform. Groups 4 , 53-95 (1999). MR 1669174 (2000f:14099)
13. Lam, T., Serre's Conjecture , Lecture Notes in Math. 635, Springer-Verlag, 1978. MR 0485842 (58:5644)
14. Raynaud, M., Modules projectifs universels, Invent. Math. 6 , 1-26 (1968). MR 0236164 (38:4462)
15. Shpilrain, V., Yu, J.T., Embeddings of hypersurfaces in affine spaces, J. of Alg. 239 , 161-173 (2001). MR 1827879 (2002m:14051)
16. Srinivas, V., On the embedding dimension of an affine variety, Math. Ann. 289 , 125-132 (1991). MR 1087241 (92a:14013)
17. Suzuki, M., Propriétés topologiques des polynômes de deux variables complexes, et automorphismes algébriques de l'espace J. Math. Soc. Japan 26 , 241-257 (1974). MR 0338423 (49:3188)
18. Swan, R.G., Vector bundles, projective modules and the MR 921488 (89f:18009)
19. Totaro, B., The automorphism group of an affine quadric, Math. Proc. Camb. Phil. Soc. 143 , 1-8 (2007). MR 2340971 (2008j:11050)
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Additional Information
Zbigniew Jelonek
Affiliation:
Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich, 00-956 Warszawa, Poland
Email:
najelone@cyf-kr.edu.pl
DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-11037-2
PII:
S 0002-9939(2011)11037-2
Keywords:
Polynomial embedding,
exotic embedding,
Zariski open subset of affine space
Received by editor(s):
January 16, 2011
Received by editor(s) in revised form:
January 26, 2011
Posted:
September 12, 2011
Additional Notes:
The author was partially supported by the Polish Ministry of Science, grant 2010-2013
Communicated by:
Lev Borisov
Article copyright:
© Copyright 2011 American Mathematical Society
has infinitely many non-equivalent embeddings into 
. Moreover, we give some examples of non-equivalent embeddings of such 
in higher codimension. 
with non-extendable automorphisms, J. Reine Angew. Math. 508, 213-235 (1999). 
to automorphisms of 
, Proc. Amer. Math. Soc. 113, 325-334 (1991). 
J. Math. Soc. Japan 26, 241-257 (1974). 
-theory of spheres, Algebraic topology and algebraic 
-theory (Princeton, N.J., 1983), 432-522, Ann. of Math. Studies 113, Princeton Univ. Press, 1987. 