메뉴 건너뛰기




Volumn 86, Issue 3, 2003, Pages 607-648

On algorithmic equi-resolution and stratification of Hilbert schemes

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0037512308     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611502013862     Document Type: Conference Paper
Times cited : (16)

References (34)
  • 1
    • 0037907046 scopus 로고
    • Remarks on equisingularity
    • S. S. ABHYANKAR, 'Remarks on equisingularity', Amer. J. Math. 90 (1968) 108-144.
    • (1968) Amer. J. Math. , vol.90 , pp. 108-144
    • Abhyankar, S.S.1
  • 2
    • 0037568991 scopus 로고
    • A criterion of equisingularity
    • S. S. ABHYANKAR, 'A criterion of equisingularity', Amer. J. Math. 90 (1968) 342-345.
    • (1968) Amer. J. Math. , vol.90 , pp. 342-345
    • Abhyankar, S.S.1
  • 3
    • 21944435825 scopus 로고    scopus 로고
    • Smoothness, semistability and toroidal geometry
    • D. ABRAMOVICH and A. J. DE JONG, 'Smoothness, semistability and toroidal geometry', J. Algebraic Geom. 6 (1997) 789-801.
    • (1997) J. Algebraic Geom. , vol.6 , pp. 789-801
    • Abramovich, D.1    De Jong, A.J.2
  • 4
    • 0031287206 scopus 로고    scopus 로고
    • Equivariant resolution of singularities in characteristic 0
    • D. ABRAMOVICH and J. WANG, 'Equivariant resolution of singularities in characteristic 0', Math. Res. Lett. 4 (1997) 427-433.
    • (1997) Math. Res. Lett. , vol.4 , pp. 427-433
    • Abramovich, D.1    Wang, J.2
  • 5
    • 33748540783 scopus 로고    scopus 로고
    • Altérations de varietés algébriques
    • Séminaire Bourbaki, Exposé No. 815
    • P. BERTHELOT, 'Altérations de varietés algébriques', Séminaire Bourbaki, Exposé No. 815, Astérisque 241 (1997) 273-311.
    • (1997) Astérisque , vol.241 , pp. 273-311
    • Berthelot, P.1
  • 6
    • 0031486450 scopus 로고    scopus 로고
    • Canonical desingularization in characteristic zero by blowing-up the maximal strata of a local invariant
    • E. BIERSTONE and P. MILMAN, 'Canonical desingularization in characteristic zero by blowing-up the maximal strata of a local invariant', Invent. Math. 128 (1997) 207-302.
    • (1997) Invent. Math. , vol.128 , pp. 207-302
    • Bierstone, E.1    Milman, P.2
  • 7
    • 0003234162 scopus 로고    scopus 로고
    • A computer program for the resolution of singularities
    • a research textbook in tribute to Oscar Zariski (ed. H. Hauser, J. Lipman, F. Oort and A. Quirós), Progress in Mathematics 181 (Birkháuser, Basel)
    • G. BODNÁR and J. SCHICHO. 'A computer program for the resolution of singularities', Resolution of singularities, a research textbook in tribute to Oscar Zariski (ed. H. Hauser, J. Lipman, F. Oort and A. Quirós), Progress in Mathematics 181 (Birkháuser, Basel, 2000) 231-238.
    • (2000) Resolution of Singularities , pp. 231-238
    • Bodnár, G.1    Schicho, J.2
  • 8
    • 0001486507 scopus 로고    scopus 로고
    • Automated resolution of singularities for hypersurfaces
    • G. BODNÁR and J. SCHICHO, 'Automated resolution of singularities for hypersurfaces', J. Symbolic Comput. 30 (2000) 401-428.
    • (2000) J. Symbolic Comput. , vol.30 , pp. 401-428
    • Bodnár, G.1    Schicho, J.2
  • 10
    • 0001604632 scopus 로고    scopus 로고
    • Good points and constructive resolution of singularities
    • S. ENCINAS and O. VILLAMAYOR, 'Good points and constructive resolution of singularities', Acta. Math. 181 (1998) 109-158.
    • (1998) Acta. Math. , vol.181 , pp. 109-158
    • Encinas, S.1    Villamayor, O.2
  • 11
    • 0012707833 scopus 로고    scopus 로고
    • A course on constructive desingularization and equivariance
    • a research textbook in tribute to Oscar Zariski (ed. H. Hauser, J. Lipman, F. Oort and A. Quirós), Progress in Mathematics 181 (Birkhäuser, Basel)
    • S. ENCINAS and O. VILLAMAYOR, 'A course on constructive desingularization and equivariance', Resolution of singularities, a research textbook in tribute to Oscar Zariski (ed. H. Hauser, J. Lipman, F. Oort and A. Quirós), Progress in Mathematics 181 (Birkhäuser, Basel, 2000) 147-227.
    • (2000) Resolution of Singularities , pp. 147-227
    • Encinas, S.1    Villamayor, O.2
  • 12
    • 85027222258 scopus 로고    scopus 로고
    • A new proof of desingularization over fields of characteristic zero
    • to appear
    • S. ENCINAS and O. VILLAMAYOR, 'A new proof of desingularization over fields of characteristic zero', Rev. Mat. Iberoamericana, to appear.
    • Rev. Mat. Iberoamericana
    • Encinas, S.1    Villamayor, O.2
  • 13
    • 27844472623 scopus 로고    scopus 로고
    • Trends in equisingularity theory
    • (ed. W. Bruce and D. Mond), London Mathematical Society Lecture Note Series 263 (Cambridge University Press)
    • T. GAFFNEY and D. MASSEY, "Trends in equisingularity theory'. Singularity theory (ed. W. Bruce and D. Mond), London Mathematical Society Lecture Note Series 263 (Cambridge University Press, 1999) 207-248.
    • (1999) Singularity Theory , pp. 207-248
    • Gaffney, T.1    Massey, D.2
  • 15
    • 0000554923 scopus 로고
    • Resolution of singularities of an algebraic variety over a field of characteristic zero I-II
    • H. HIRONAKA, 'Resolution of singularities of an algebraic variety over a field of characteristic zero I-II', Ann. of Math. 79 (1964) 109-326.
    • (1964) Ann. of Math. , vol.79 , pp. 109-326
    • Hironaka, H.1
  • 16
    • 0002684684 scopus 로고
    • Idealistic exponent of a singularity
    • (ed. Jun-Ichi Igusa), The John Hopkins centennial lectures (Johns Hopkins University Press, Baltimore)
    • H. HIRONAKA, 'Idealistic exponent of a singularity', Algebraic geometry (ed. Jun-Ichi Igusa), The John Hopkins centennial lectures (Johns Hopkins University Press, Baltimore, 1977) 52-125.
    • (1977) Algebraic Geometry , pp. 52-125
    • Hironaka, H.1
  • 18
    • 0002629494 scopus 로고    scopus 로고
    • Equisingularity, multiplicity and dependence
    • (ed. F. van Oystaeyen), Lecture Notes in Pure and Applied Mathematics 206 (Dekker, New York)
    • S. KLEIMAN, 'Equisingularity, multiplicity and dependence', Commutative algebra and algebraic geometry (ed. F. van Oystaeyen), Lecture Notes in Pure and Applied Mathematics 206 (Dekker, New York, 1999) 211-225.
    • (1999) Commutative Algebra and Algebraic Geometry , pp. 211-225
    • Kleiman, S.1
  • 19
    • 85008283679 scopus 로고
    • Strong simultaneous resolution for surface singularities
    • ed. T. Suwa and P. Wagreich, North-Holland, Amsterdam
    • H. LAUFER, 'Strong simultaneous resolution for surface singularities', Complex analytic singularities (ed. T. Suwa and P. Wagreich, North-Holland, Amsterdam, 1987) 207-214.
    • (1987) Complex Analytic Singularities , pp. 207-214
    • Laufer, H.1
  • 20
    • 27344450780 scopus 로고    scopus 로고
    • Equisingularity and simultaneous resolution of singularities
    • a research textbook in tribute to Oscar Zariski (ed. H. Hauser, J. Lipman, F. Oort and A. Quirós), Progress in Mathematics 181 (Birkhäuser, Basel)
    • J. LIPMAN, 'Equisingularity and simultaneous resolution of singularities', Resolution of singularities, a research textbook in tribute to Oscar Zariski (ed. H. Hauser, J. Lipman, F. Oort and A. Quirós), Progress in Mathematics 181 (Birkhäuser, Basel, 2000) 485-505.
    • (2000) Resolution of Singularities , pp. 485-505
    • Lipman, J.1
  • 21
    • 0010127895 scopus 로고
    • Commutative algebra, 2nd edn
    • Benjamin/Cummings, Reading, MA
    • H. MATSUMURA, Commutative algebra, 2nd edn, Mathematics Lecture Note Series 56 (Benjamin/Cummings, Reading, MA, 1980).
    • (1980) Mathematics Lecture Note Series , vol.56
    • Matsumura, H.1
  • 22
    • 0003340499 scopus 로고
    • Geometric invariant theory
    • Springer, Berlin
    • D. MUMFORD, Geometric invariant theory, Ergebnisse der Mathematik 34 (Springer, Berlin, 1965).
    • (1965) Ergebnisse der Mathematik , vol.34
    • Mumford, D.1
  • 23
    • 0038583242 scopus 로고    scopus 로고
    • Equisingular stratifications of parameter spaces of families of embedded curves
    • (ed. N. Andruskiewitsch and J. A. Vargas), Boletín de la Academia National de Ciencias 65 (Córdoba, Argentina)
    • A. NOBILE, 'Equisingular stratifications of parameter spaces of families of embedded curves', Proceedings of a conference in honor of O. E. Villamayor Sr (ed. N. Andruskiewitsch and J. A. Vargas), Boletín de la Academia National de Ciencias 65 (Córdoba, Argentina, 2000) 189-198.
    • (2000) Proceedings of a Conference in Honor of O. E. Villamayor Sr , pp. 189-198
    • Nobile, A.1
  • 24
    • 0031185261 scopus 로고    scopus 로고
    • Equisingular stratifications associated to families of planar ideals
    • A. NOBILE and O. E. VILLAMAYOR, 'Equisingular stratifications associated to families of planar ideals', J. Algebra 193 (1997) 239-259.
    • (1997) J. Algebra , vol.193 , pp. 239-259
    • Nobile, A.1    Villamayor, O.E.2
  • 25
    • 0033468019 scopus 로고    scopus 로고
    • Arithmetic families of smooth surfaces and equisingularity of embedded schemes
    • A. NOBILE and O. E. VILLAMAYOR, 'Arithmetic families of smooth surfaces and equisingularity of embedded schemes', Manuscripta Math. 100 (1999) 173-196.
    • (1999) Manuscripta Math. , vol.100 , pp. 173-196
    • Nobile, A.1    Villamayor, O.E.2
  • 27
    • 0039677454 scopus 로고
    • Résolution simultanée
    • (ed. M. Demazure, H. Pinkham and B. Teissier), Lecture Notes in Mathematics 777 (Springer, Berlin)
    • B. TEISSIER, 'Résolution simultanée', Séminaire sur les singularités de surfaces (ed. M. Demazure, H. Pinkham and B. Teissier), Lecture Notes in Mathematics 777 (Springer, Berlin, 1980) 82-146.
    • (1980) Séminaire sur les Singularités de Surfaces , pp. 82-146
    • Teissier, B.1
  • 28
    • 0003287040 scopus 로고
    • Constructiveness of Hironaka's resolution
    • O. E. VILLAMAYOR, 'Constructiveness of Hironaka's resolution", Ann. Sci. École Norm. Sup. (4) 22 (1989) 1-32.
    • (1989) Ann. Sci. École Norm. Sup. , vol.22 , Issue.4 , pp. 1-32
    • Villamayor, O.E.1
  • 30
    • 0037568986 scopus 로고    scopus 로고
    • On equiresolution and a question of Zariski
    • O. E. VILLAMAYOR, 'On equiresolution and a question of Zariski', Acta Math. 185 (2000) 123-159.
    • (2000) Acta Math. , vol.185 , pp. 123-159
    • Villamayor, O.E.1
  • 31
    • 0000954050 scopus 로고
    • Equisingular deformations of normal surface singularities
    • J. WAHL, 'Equisingular deformations of normal surface singularities', Ann. of Math. 104 (1976) 325-356.
    • (1976) Ann. of Math. , vol.104 , pp. 325-356
    • Wahl, J.1
  • 32
    • 0001292757 scopus 로고
    • Some open questions in the theory of singularities
    • O. ZARISKI, 'Some open questions in the theory of singularities', Bull. Amer. Math. Soc. 77 (1971) 481-491.
    • (1971) Bull. Amer. Math. Soc. , vol.77 , pp. 481-491
    • Zariski, O.1
  • 33
    • 0038244563 scopus 로고
    • Foundations of a general theory of equisingularity on r-dimensional algebroid and algebraic varieties, of embedded dimension r+1
    • reprinted in [34, pp. 573-634] and summarized in [34, pp. 635-651]
    • O. ZARISKI, 'Foundations of a general theory of equisingularity on r-dimensional algebroid and algebraic varieties, of embedded dimension r+1', Amer. J. Math. 101 (1979) 453-514 (reprinted in [34, pp. 573-634] and summarized in [34, pp. 635-651]).
    • (1979) Amer. J. Math. , vol.101 , pp. 453-514
    • Zariski, O.1
  • 34
    • 0003946760 scopus 로고
    • MIT Press, Cambridge, MA
    • O. ZARISKI. Collected papers, vol. IV (MIT Press, Cambridge, MA, 1979).
    • (1979) Collected Papers , vol.4
    • Zariski, O.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.