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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Conditions for the existence of contractions in the category of algebraic spaces
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by Joseph Mazur PDF
Trans. Amer. Math. Soc. 209 (1975), 259-265 Request permission


Artin’s conditions for the existence of a new contraction of an algebraic subspace are changed. The new conditions are more applicable in special cases, especially when the subspace has a conormal bundle.
  • M. Artin, Algebraization of formal moduli. II. Existence of modifications, Ann. of Math. (2) 91 (1970), 88–135. MR 260747, DOI 10.2307/1970602
  • M. Artin, The implicit function theorem in algebraic geometry, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968) Oxford Univ. Press, London, 1969, pp. 13–34. MR 0262237
  • —, Algebraic spaces, Whittemore Lectures, Yale University, 1969 (mimeographed notes). N. Bourbaki, Éléments de mathématiques. Fasc. XXVIII. Algèbre commutative. Chap. 3: Graduations, filtrations et topoligies, Actualités Sci. Indust., no. 1293, Hermann, Paris, 1961. MR 30 #2027. J. Dieudonné and A. Grothendieck, Éléments de géométrie algébrique, Inst. Hautes Études Sci. Publ. Math. Nos. 8, 11 (1960/61). MR 36 #177b, c.
  • Hans Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368 (German). MR 137127, DOI 10.1007/BF01441136
  • Robin Hartshorne, Ample vector bundles, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 63–94. MR 193092
  • Robin Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-New York, 1970. Notes written in collaboration with C. Musili. MR 0282977, DOI 10.1007/BFb0067839
  • Donald Knutson, Algebraic spaces, Lecture Notes in Mathematics, Vol. 203, Springer-Verlag, Berlin-New York, 1971. MR 0302647, DOI 10.1007/BFb0059750
  • J. Mazur, A relative étale topology for imbedded subschemes (to appear).
  • Jean-Pierre Serre, Faisceaux algébriques cohérents, Ann. of Math. (2) 61 (1955), 197–278 (French). MR 68874, DOI 10.2307/1969915
  • O. Zariski, Algebraic surfaces, Springer, Berlin, 1935.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 209 (1975), 259-265
  • MSC: Primary 14E15; Secondary 14A20
  • DOI:
  • MathSciNet review: 0387280