Singularities on complete algebraic varieties

• Autorzy: Fedor Bogomolov , Paolo Cascini , Bruno Oliveira
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Isolated singularities; deformation of singularities; 14B05; 32S05

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 2
• Strony: 194-208

Daty

wydano

2006-06-01

online

2006-06-01

Twórcy

autor

Fedor Bogomolov

• Courant Institute of Mathematical Sciences,

autor

Paolo Cascini

• UC Santa Barbara,

autor

Bruno Oliveira

• University of Miami,

Bibliografia

• [1] M. Artin: “On the solutions of analytic equations”, Invent. Math., Vol. 5, (1968), pp. 277–291. http://dx.doi.org/10.1007/BF01389777
• [2] M. Artin: “Algebraic approximation of structures over complete local rings”, Publ. Math. I.H.E.S., Vol. 36, (1969), pp. 23–58.
• [3] F.A. Bogomolov and T. Pantev: “Weak Hironaka Theorem”, Math. Res. Let., Vol. 3, (1996), pp. 299–307.
• [4] C. Ciliberto and S. Greco: “On normal surface singularities and a problem of Enriques”, Commun. Algebra, Vol. 28(12), (2000), pp. 5891–5913.
• [5] C. Epstein and G. Henkin: “Stability of embeddings for pseudoconcave surfaces and their boundaries”, Acta Math., Vol. 185(2), (2000), pp. 161–237.
• [6] M J. Mather: Notes on Topological Stability, Mimeographed Notes, Harvard University, 1970.
• [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
• [8] R. Hartdt: “Topological Properties of subanalytic sets”, Trans. Amer. Math. Soc., Vol. 211, (1975), pp. 193–208.
• [9] L. Lempert: “Algebraic approximations in analytic geometry”, Inv. Math., Vol. 121(2), (1995), pp. 335–353.
• [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.
• [11] F. Sakai: “Weil divisors on normal surfaces”, Duke Math., Vol. 51, (1984), pp. 877–887.
• [12] F. Sakai: “The structure of normal surfaces”, Duke Math., Vol. 52, (1985), pp. 627–648.
• [13] H. Whitney: Local Properties of Analytic Varieties, Differential and Combinatorial Topology, Princeton Univ. Press, Princeton N.J., 1965, pp. 205–244.

Identyfikatory

DOI

10.2478/s11533-006-0005-x