Bulletin of the American Mathematical Society

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Book Information:

Author: Steven Dale Cutkosky
Title: Resolution of singularities
Additional book information: Graduate Studies in Mathematics, 63, American Mathematical Society, Providence, RI, 2004, viii+186 pp., ISBN 978-0-8218-3555-5, US$41.00

Author: János Kollár
Title: Lectures on resolution of singularities
Additional book information: Annals of Mathematics Studies, 166, Princeton University Press, Princeton, New Jersey, 2007, vi+208 pp., ISBN 978-0-691-12923-5, US$42.00

Shreeram Shankar Abhyankar, Resolution of singularities of embedded algebraic surfaces, Pure and Applied Mathematics, Vol. 24, Academic Press, New York-London, 1966. MR 0217069

D. Abramovich and A. J. de Jong, Smoothness, semistability, and toroidal geometry, J. Algebraic Geom. 6 (1997), no. 4, 789–801. MR 1487237

D. Abramovich and K. Karu, Weak semistable reduction in characteristic 0, Invent. Math. 139 (2000), no. 2, 241–273. MR 1738451, DOI 10.1007/s002229900024

Edward Bierstone and Pierre D. Milman, Uniformization of analytic spaces, J. Amer. Math. Soc. 2 (1989), no. 4, 801–836. MR 1001853, DOI 10.1090/S0894-0347-1989-1001853-2

Edward Bierstone and Pierre D. Milman, Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Invent. Math. 128 (1997), no. 2, 207–302. MR 1440306, DOI 10.1007/s002220050141

Fedor A. Bogomolov and Tony G. Pantev, Weak Hironaka theorem, Math. Res. Lett. 3 (1996), no. 3, 299–307. MR 1397679, DOI 10.4310/MRL.1996.v3.n3.a1

Vincent Cossart, Jean Giraud, and Ulrich Orbanz, Resolution of surface singularities, Lecture Notes in Mathematics, vol. 1101, Springer-Verlag, Berlin, 1984. With an appendix by H. Hironaka. MR 775681, DOI 10.1007/BFb0072258

Vincent Cossart, Uwe Jannsen, and Shuji Saito. Canonical embedded and non-embedded resolution of singularities for excellent two-dimensional schemes, 2009. preprint arXiv:0905.2191.

Vincent Cossart and Olivier Piltant, Resolution of singularities of threefolds in positive characteristic. I. Reduction to local uniformization on Artin-Schreier and purely inseparable coverings, J. Algebra 320 (2008), no. 3, 1051–1082. MR 2427629, DOI 10.1016/j.jalgebra.2008.03.032

Vincent Cossart and Olivier Piltant, Resolution of singularities of threefolds in positive characteristic. II, J. Algebra 321 (2009), no. 7, 1836–1976. MR 2494751, DOI 10.1016/j.jalgebra.2008.11.030

Steven Dale Cutkosky, Resolution of singularities, Graduate Studies in Mathematics, vol. 63, American Mathematical Society, Providence, RI, 2004. MR 2058431, DOI 10.1090/gsm/063

Steven Dale Cutkosky, The structure of morphisms, Algebra, arithmetic and geometry with applications (West Lafayette, IN, 2000) Springer, Berlin, 2004, pp. 273–281. MR 2037094

Steven Dale Cutkosky, Resolution of singularities for 3-folds in positive characteristic, Amer. J. Math. 131 (2009), no. 1, 59–127. MR 2488485, DOI 10.1353/ajm.0.0036

Santiago Encinas and Orlando Villamayor, A course on constructive desingularization and equivariance, Resolution of singularities (Obergurgl, 1997) Progr. Math., vol. 181, Birkhäuser, Basel, 2000, pp. 147–227. MR 1748620

Jean Giraud, Sur la théorie du contact maximal, Math. Z. 137 (1974), 285–310 (French). MR 460712, DOI 10.1007/BF01214371

A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. II, Inst. Hautes Études Sci. Publ. Math. 24 (1965), 231 (French). MR 199181

A. Grothendieck, Travaux de Heisouké Hironaka sur la résolution des singularités, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 7–9 (French). MR 0414283

Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157

Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109–203; ibid. (2) 79 (1964), 205–326. MR 0199184, DOI 10.2307/1970547

Herwig Hauser, Three power series techniques, Proc. London Math. Soc. (3) 89 (2004), no. 1, 1–24. MR 2063657, DOI 10.1112/S0024611503014588

A. J. de Jong, Smoothness, semi-stability and alterations, Inst. Hautes Études Sci. Publ. Math. 83 (1996), 51–93. MR 1423020

János Kollár, Lectures on resolution of singularities, Annals of Mathematics Studies, vol. 166, Princeton University Press, Princeton, NJ, 2007. MR 2289519

János Kollár and Shigefumi Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Cambridge, 1998. With the collaboration of C. H. Clemens and A. Corti; Translated from the 1998 Japanese original. MR 1658959, DOI 10.1017/CBO9780511662560

Joseph Lipman, Introduction to resolution of singularities, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) Amer. Math. Soc., Providence, R.I., 1975, pp. 187–230. MR 0389901

Joseph Lipman, Desingularization of two-dimensional schemes, Ann. of Math. (2) 107 (1978), no. 1, 151–207. MR 491722, DOI 10.2307/1971141

Mircea Mustaţă. Lectures on resolution of singularities, 2010. IAS/Park City Mathematics Series, to appear.

Kapil H. Paranjape, The Bogomolov-Pantev resolution, an expository account, New trends in algebraic geometry (Warwick, 1996) London Math. Soc. Lecture Note Ser., vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 347–358. MR 1714830, DOI 10.1017/CBO9780511721540.014

Michael Temkin, Desingularization of quasi-excellent schemes in characteristic zero, Adv. Math. 219 (2008), no. 2, 488–522. MR 2435647, DOI 10.1016/j.aim.2008.05.006

Orlando Villamayor, Constructiveness of Hironaka’s resolution, Ann. Sci. École Norm. Sup. (4) 22 (1989), no. 1, 1–32. MR 985852, DOI 10.24033/asens.1573

Jarosław Włodarczyk, Simple Hironaka resolution in characteristic zero, J. Amer. Math. Soc. 18 (2005), no. 4, 779–822. MR 2163383, DOI 10.1090/S0894-0347-05-00493-5

• Shreeram Shankar Abhyankar. Resolution of singularities of embedded algebraic surfaces. Pure and Applied Mathematics, Vol. 24. Academic Press, New York, 1966. MR 0217069 (36:164)
• D. Abramovich and A. J. de Jong. Smoothness, semistability, and toroidal geometry. J. Algebraic Geom., 6(4):789–801, 1997. MR 1487237 (99b:14016)
• D. Abramovich and K. Karu. Weak semistable reduction in characteristic 0. Invent. Math., 139(2):241–273, 2000. MR 1738451 (2001f:14021)
• Edward Bierstone and Pierre D. Milman. Uniformization of analytic spaces. J. Amer. Math. Soc., 2(4):801–836, 1989. MR 1001853 (91c:32033)
• Edward Bierstone and Pierre D. Milman. Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant. Invent. Math., 128(2):207–302, 1997. MR 1440306 (98e:14010)
• Fedor A. Bogomolov and Tony G. Pantev. Weak Hironaka theorem. Math. Res. Lett., 3(3):299–307, 1996. MR 1397679 (97e:14024)
• Vincent Cossart, Jean Giraud, and Ulrich Orbanz. Resolution of surface singularities, volume 1101 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1984. With an appendix by H. Hironaka. MR 775681 (87e:14032)
• Vincent Cossart, Uwe Jannsen, and Shuji Saito. Canonical embedded and non-embedded resolution of singularities for excellent two-dimensional schemes, 2009. preprint arXiv:0905.2191.
• Vincent Cossart and Olivier Piltant. Resolution of singularities of threefolds in positive characteristic. I. Reduction to local uniformization on Artin-Schreier and purely inseparable coverings. J. Algebra, 320(3):1051–1082, 2008. MR 2427629 (2009f:14024)
• Vincent Cossart and Olivier Piltant. Resolution of singularities of threefolds in positive characteristic. II. J. Algebra, 321(7):1836–1976, 2009. MR 2494751 (2010c:14009)
• Steven Dale Cutkosky. Resolution of singularities, Graduate Studies in Mathematics, 63. American Mathematical Society, Providence, RI, 2004. MR 2058431 (2005d:14022)
• Steven Dale Cutkosky. The structure of morphisms. In Algebra, arithmetic and geometry with applications (West Lafayette, IN, 2000), pages 273–281. Springer, Berlin, 2004. MR 2037094 (2005e:14019)
• Steven Dale Cutkosky. Resolution of singularities for 3-folds in positive characteristic. Amer. J. Math., 131(1):59–127, 2009. MR 2488485
• Santiago Encinas and Orlando Villamayor. A course on constructive desingularization and equivariance. In Resolution of singularities (Obergurgl, 1997), volume 181 of Progr. Math., pages 147–227. Birkhäuser, Basel, 2000. MR 1748620 (2001g:14018)
• Jean Giraud. Sur la théorie du contact maximal. Math. Z., 137:285–310, 1974. MR 0460712 (57:705)
• A. Grothendieck. Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. II. Inst. Hautes Études Sci. Publ. Math., 24:231, 1965. MR 0199181 (33:7330)
• A. Grothendieck. Travaux de Heisouké Hironaka sur la résolution des singularités. In Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1, pages 7–9. Gauthier-Villars, Paris, 1971. MR 0414283 (54:2386)
• Robin Hartshorne. Algebraic geometry. Springer-Verlag, New York, 1977. Graduate Texts in Mathematics, No. 52. MR 0463157 (57:3116)
• Heisuke Hironaka. Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II. Ann. of Math. (2) 79 (1964), 109–203; ibid. (2), 79 (1964), 205–326. MR 0199184 (33:7333)
• Herwig Hauser. Three power series techniques. Proc. London Math. Soc. (3) 89 (2004), no. 1, 1–24. MR 2063657 (2005f:14032)
• A. J. de Jong. Smoothness, semi-stability and alterations. Inst. Hautes Études Sci. Publ. Math., 83:51–93, 1996. MR 1423020 (98e:14011)
• János Kollár. Lectures on resolution of singularities, Annals of Mathematics Studies, 166. Princeton University Press, Princeton, NJ, 2007. MR 2289519 (2008f:14026)
• János Kollár and Shigefumi Mori. Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134. Cambridge University Press, Cambridge, 1998. With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original. MR 1658959 (2000b:14018)
• Joseph Lipman. Introduction to resolution of singularities. In Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974), pages 187–230. Amer. Math. Soc., Providence, R.I., 1975. MR 0389901 (52:10730)
• Joseph Lipman. Desingularization of two-dimensional schemes. Ann. Math. (2), 107(1):151–207, 1978. MR 0491722 (58:10924)
• Mircea Mustaţă. Lectures on resolution of singularities, 2010. IAS/Park City Mathematics Series, to appear.
• Kapil H. Paranjape. The Bogomolov-Pantev resolution, an expository account. In New trends in algebraic geometry (Warwick, 1996), volume 264 of London Math. Soc. Lecture Note Ser., pages 347–358. Cambridge Univ. Press, Cambridge, 1999. MR 1714830 (2000g:14023)
• Michael Temkin. Desingularization of quasi-excellent schemes in characteristic zero. Adv. Math., 219(2):488–522, 2008. MR 2435647 (2009h:14027)
• Orlando Villamayor. Constructiveness of Hironaka’s resolution. Ann. Sci. École Norm. Sup. (4), 22(1):1–32, 1989. MR 985852 (90b:14014)
• Jarosław Włodarczyk. Simple Hironaka resolution in characteristic zero. J. Amer. Math. Soc., 18(4):779–822 (electronic), 2005. MR 2163383 (2006f:14014)