Singularities on complete algebraic varieties

Fedor Bogomolov; Paolo Cascini; Bruno Oliveira

Open Mathematics (2006)

  • Volume: 4, Issue: 2, page 194-208
  • ISSN: 2391-5455

Abstract

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We prove that any finite set of n-dimensional isolated algebraic singularities can be afforded on a simply connected projective variety.

How to cite

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Fedor Bogomolov, Paolo Cascini, and Bruno Oliveira. "Singularities on complete algebraic varieties." Open Mathematics 4.2 (2006): 194-208. <http://eudml.org/doc/269576>.

@article{FedorBogomolov2006,
abstract = {We prove that any finite set of n-dimensional isolated algebraic singularities can be afforded on a simply connected projective variety.},
author = {Fedor Bogomolov, Paolo Cascini, Bruno Oliveira},
journal = {Open Mathematics},
keywords = {14B05; 32S05},
language = {eng},
number = {2},
pages = {194-208},
title = {Singularities on complete algebraic varieties},
url = {http://eudml.org/doc/269576},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Fedor Bogomolov
AU - Paolo Cascini
AU - Bruno Oliveira
TI - Singularities on complete algebraic varieties
JO - Open Mathematics
PY - 2006
VL - 4
IS - 2
SP - 194
EP - 208
AB - We prove that any finite set of n-dimensional isolated algebraic singularities can be afforded on a simply connected projective variety.
LA - eng
KW - 14B05; 32S05
UR - http://eudml.org/doc/269576
ER -

References

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  1. [1] M. Artin: “On the solutions of analytic equations”, Invent. Math., Vol. 5, (1968), pp. 277–291. http://dx.doi.org/10.1007/BF01389777 Zbl0172.05301
  2. [2] M. Artin: “Algebraic approximation of structures over complete local rings”, Publ. Math. I.H.E.S., Vol. 36, (1969), pp. 23–58. Zbl0181.48802
  3. [3] F.A. Bogomolov and T. Pantev: “Weak Hironaka Theorem”, Math. Res. Let., Vol. 3, (1996), pp. 299–307. Zbl0869.14007
  4. [4] C. Ciliberto and S. Greco: “On normal surface singularities and a problem of Enriques”, Commun. Algebra, Vol. 28(12), (2000), pp. 5891–5913. Zbl1017.14011
  5. [5] C. Epstein and G. Henkin: “Stability of embeddings for pseudoconcave surfaces and their boundaries”, Acta Math., Vol. 185(2), (2000), pp. 161–237. Zbl0983.32035
  6. [6] M J. Mather: Notes on Topological Stability, Mimeographed Notes, Harvard University, 1970. 
  7. [7] D. Morrison: “The birational geometry of surfaces with rational double points”, Math. Ann., Vol. 271, (1985), pp. 415–438. http://dx.doi.org/10.1007/BF01456077 Zbl0539.14008
  8. [8] R. Hartdt: “Topological Properties of subanalytic sets”, Trans. Amer. Math. Soc., Vol. 211, (1975), pp. 193–208. 
  9. [9] L. Lempert: “Algebraic approximations in analytic geometry”, Inv. Math., Vol. 121(2), (1995), pp. 335–353. Zbl0837.32008
  10. [10] N. Levinson: “A polynomial canonical form for certain analytic functions of two variables at a critical point”, Bull. Am. Math. Soc., Vol. 66, (1960), 366–368. Zbl0192.18202
  11. [11] F. Sakai: “Weil divisors on normal surfaces”, Duke Math., Vol. 51, (1984), pp. 877–887. Zbl0602.14006
  12. [12] F. Sakai: “The structure of normal surfaces”, Duke Math., Vol. 52, (1985), pp. 627–648. Zbl0596.14025
  13. [13] H. Whitney: Local Properties of Analytic Varieties, Differential and Combinatorial Topology, Princeton Univ. Press, Princeton N.J., 1965, pp. 205–244. 

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