Smoothings of schemes with nonisolated singularities
Nikolaos Tziolas
Source: Michigan Math. J. Volume 59, Issue 1
(2010), 25-84.
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References
V. Alexeev, Higher-dimensional analogues of stable curves, International Congress of Mathematicians, vol. II, pp. 515--536, European Mathematical Society, Zürich, 2006.
Mathematical Reviews (MathSciNet): MR2275608
Zentralblatt MATH: 1102.14023
M. Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 23--58.
Mathematical Reviews (MathSciNet): MR268188
Digital Object Identifier: doi:10.1007/BF02684596
------, Deformations of singularities, Tata Inst. Fund. Res. Lectures on Math. and Phys., 54, Tata Inst. Fund. Res., Bombay, 1976.
D. Cox, Algebraic tubular neighborhoods I, Math. Scand. 42 (1978), 211--228.
Mathematical Reviews (MathSciNet): MR512271
D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Grad. Texts in Math., 150, Springer-Verlag, New York, 1995.
Mathematical Reviews (MathSciNet): MR1322960
B. Fantechi and M. Manetti, Obstruction calculus for functors of Artin rings, I, J. Algebra 202 (1998), 541--576.
Mathematical Reviews (MathSciNet): MR1617687
Zentralblatt MATH: 0981.13009
Digital Object Identifier: doi:10.1006/jabr.1997.7239
------, On the $T^1$-lifting theorem, J. Algebraic Geom. 8 (1999), 31--39.
Mathematical Reviews (MathSciNet): MR1658200
Zentralblatt MATH: 0974.13013
R. Friedman, Global smoothings of varieties with normal crossings, Ann. of Math. (2) 118 (1983), 75--114.
Mathematical Reviews (MathSciNet): MR707162
Digital Object Identifier: doi:10.2307/2006955
JSTOR: links.jstor.org
H. Grauert, Über die Deformationen isolierter singularitäten analytischer Mengen, Invent. Math. 25 (1972), 171--198.
Mathematical Reviews (MathSciNet): MR293127
Digital Object Identifier: doi:10.1007/BF01404124
------, Der Satz von Kuranishi für kompakte komplexe Räume, Invent. Math. 25 (1974), 107--142.
Mathematical Reviews (MathSciNet): MR346194
Digital Object Identifier: doi:10.1007/BF01390171
A. Grothendieck, Eléments de géométrie algébrique IV, Inst. Hautes Études Sci. Publ. Math. 20 (1964).
------, Géométrie formelle et géométrie algébrique, Séminaire Bourbaki, 5, pp. 193--220, Soc. Math. France, Paris, 1995.
Mathematical Reviews (MathSciNet): MR1603467
P. Hacking, Compact moduli of plane curves, Duke Math. J. 124 (2004), 213--257.
Mathematical Reviews (MathSciNet): MR2078368
Zentralblatt MATH: 1060.14034
Digital Object Identifier: doi:10.1215/S0012-7094-04-12421-2
Project Euclid: euclid.dmj/1091735975
M. Halperin, Deformations of formal embeddings of schemes, Trans. Amer. Math. Soc. 221 (1976), 303--321.
Mathematical Reviews (MathSciNet): MR407016
Zentralblatt MATH: 0355.14006
R. Hartshorne, Cohomological dimension of algebraic varieties, Ann. of Math. (2) 88 (1968), 403--450.
Mathematical Reviews (MathSciNet): MR232780
Digital Object Identifier: doi:10.2307/1970720
JSTOR: links.jstor.org
------, Algebraic geometry, Grad. Texts in Math., 52, Springer-Verlag, New York, 1977.
------, Lectures on deformation theory, preprint, 2004.
B. Hassett and S. Kovács, Reflexive pull-backs and base extension, J. Algebraic Geom. 13 (2004), 233--247.
Mathematical Reviews (MathSciNet): MR2047697
Zentralblatt MATH: 1081.14017
Y. Kawamata, Unobstructed deformations---A remark on a paper of Z. Ran, J. Algebraic Geom. 1 (1992), 183--190.
Mathematical Reviews (MathSciNet): MR1144434
------, Erratum on unobstructed deformations, J. Algebraic Geom. 6 (1997), 803--804.
Mathematical Reviews (MathSciNet): MR1487238
Y. Kawamata and Y. Namikawa, Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi--Yau varieties, Invent. Math. 118 (1994), 395--409.
Mathematical Reviews (MathSciNet): MR1296351
Zentralblatt MATH: 0848.14004
Digital Object Identifier: doi:10.1007/BF01231538
J. Kollár and S. Mori, Classification of three-dimensional flips, J. Amer. Math. Soc. 5 (1992), 533--703.
Mathematical Reviews (MathSciNet): MR1149195
JSTOR: links.jstor.org
J. Kollár and N. I. Shepherd-Barron, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988), 299--338.
Mathematical Reviews (MathSciNet): MR922803
Zentralblatt MATH: 0642.14008
Digital Object Identifier: doi:10.1007/BF01389370
S. Lichtenbaum and M. Schlessinger, The cotangent complex of a morphism, Trans. Amer. Math. Soc. 128 (1967), 41--70.
J. Lipman, J. Nayak, and S. Sastry, Pseudofunctorial behavior of Cousin complexes on formal schemes, Variance and duality for Cousin complexes on formal schemes, Contemp. Math., 375, pp. 3--133, Amer. Math. Soc., Providence, RI, 2005.
Mathematical Reviews (MathSciNet): MR2136143
Zentralblatt MATH: 1080.14005
Y. Namikawa, On deformations of $Q$-factorial symplectic varieties, J. Reine Angew. Math. 599 (2006), 97--110.
Mathematical Reviews (MathSciNet): MR2279099
H. Pinkham and U. Persson, Some examples of nonsmoothable varieties with normal crossings, Duke Math. J. 50 (1983), 477--486.
Mathematical Reviews (MathSciNet): MR705035
Zentralblatt MATH: 0529.14007
Digital Object Identifier: doi:10.1215/S0012-7094-83-05020-2
Project Euclid: euclid.dmj/1077303204
Z. Ran, Deformations of manifolds with torsion or negative canonical bundle, J. Algebraic Geom. 1 (1992), 279--291.
Mathematical Reviews (MathSciNet): MR1144440
Zentralblatt MATH: 0818.14003
M. Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208--222.
E. Sernesi, Deformations of algebraic schemes, Grundlehren Math. Wiss., 334, Springer-Verlag, Berlin, 2006.
Mathematical Reviews (MathSciNet): MR2247603
Zentralblatt MATH: 1102.14001
L. A. Tarrío, A. J. López, and M. P. Rodríguez, Infinitesimal lifting and Jacobi criterion for smoothness on formal schemes, Comm. Algebra 35 (2007), 1341--1367.
Mathematical Reviews (MathSciNet): MR2313672
Zentralblatt MATH: 1124.14006
Digital Object Identifier: doi:10.1080/00927870601115823
N. Tziolas, $\Bbb Q$-Gorenstein smoothings of nonnormal surfaces, Amer. J. Math. 131 (2009), 171--193.
Mathematical Reviews (MathSciNet): MR2488488
Zentralblatt MATH: 1162.14005
------, Smoothings of normal crossing Fano schemes of dimension at most three, preprint, 2009, arXiv:0907.3641v1.
J. Wahl, Equisingular deformations of normal surface singularities I, Ann. of Math. (2) 104 (1976), 325--356.
Mathematical Reviews (MathSciNet): MR422270
Digital Object Identifier: doi:10.2307/1971049
JSTOR: links.jstor.org
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