Hypersurface sections and obstructions (rational surface singularities)

Kurt Behnke; Jan Arthur Christophersen

Compositio Mathematica (1991)

  • Volume: 77, Issue: 3, page 233-268
  • ISSN: 0010-437X

How to cite

top

Behnke, Kurt, and Christophersen, Jan Arthur. "Hypersurface sections and obstructions (rational surface singularities)." Compositio Mathematica 77.3 (1991): 233-268. <http://eudml.org/doc/90073>.

@article{Behnke1991,
author = {Behnke, Kurt, Christophersen, Jan Arthur},
journal = {Compositio Mathematica},
keywords = {obstruction to deformations; rational singularities; isolated singularity},
language = {eng},
number = {3},
pages = {233-268},
publisher = {Kluwer Academic Publishers},
title = {Hypersurface sections and obstructions (rational surface singularities)},
url = {http://eudml.org/doc/90073},
volume = {77},
year = {1991},
}

TY - JOUR
AU - Behnke, Kurt
AU - Christophersen, Jan Arthur
TI - Hypersurface sections and obstructions (rational surface singularities)
JO - Compositio Mathematica
PY - 1991
PB - Kluwer Academic Publishers
VL - 77
IS - 3
SP - 233
EP - 268
LA - eng
KW - obstruction to deformations; rational singularities; isolated singularity
UR - http://eudml.org/doc/90073
ER -

References

top
  1. 1 Oscar Zariski, Studies in equisingularity I. Equivalent singularities of plane algebroid curves, Amer. J. Math.87 (1965), 507-536. Zbl0132.41601MR177985
  2. [Aleksandrov] Aleksandrov, A.G., On deformations of one-dimensional singularities with c = δ + 1, Russian Math. Surveys33:3 (1978), 139-140. Zbl0399.14021
  3. [André] André, M., Homologie des algèbres commutatives, Grundlehren der mathematischen Wissenschaften, Bd. 206, Springer, Berlin- Heidelberg-New York. Zbl0284.18009MR352220
  4. [Arndt] Arndt, J., Verselle Deformationen zyklischer Quotientensingularitäten, Dissertation, Universität Hamburg, 1988. 
  5. [Artin 1] Artin, M., On isolated rational singularities of surfaces, American Journal of Math.88 (1966), 129-136. Zbl0142.18602MR199191
  6. [Artin 2] Artin, M., Deformations of singularities, Tata Lecture Notes. Zbl0352.14007
  7. [Artin-Verdier] Artin, M., Verdier, J.L., Reflexive modules over rational double points, Math. Ann.270 (1985), 79-82. Zbl0553.14001MR769609
  8. [Bayer-Christophersen] Bayer, D., Christophersen, J.A., In preparation. 
  9. [Behnke] Behnke, K., Infinitesimal deformations of cusp singularities, Math. Annalen265 (1983), 407-422. Zbl0559.14001MR721879
  10. [Behnke-Kahn-Riemenschneider] Behnke, K., Kahn, C., Riemenschneider, O., Infinitesimal deformations of quotient surface singularities, in ' Singularities,' Banach Center Publications, Polish Scientific Publishers, Warzaw, 1989, pp. 31-66. Zbl0668.32020MR1101829
  11. [Behnke-Knörrer] Behnke, K., Knörrer, H., On the infinitesimal deformations of rational surface singularities, Compositio Math.61 (1987), 103-127. Zbl0615.14001MR879191
  12. [Brieskorn] Brieskorn, E., Rationale Singularitäten komplexer Flächen, Inventiones Math.4 (1968), 336-358. Zbl0219.14003MR222084
  13. [Brieskorn-Knörrer] Brieskorn, E., Knörrer, H., Ebene Algebraische Kurven, Birkhäuser, Basel. Zbl0508.14018MR646612
  14. [Buchweitz] Buchweitz, R.O., Deformations de diagrammes, deploiments et singularités très rigides, liaison algébrique, Thèses présentées à l'Université ParisVII, 1981. 
  15. [Buchweitz-Greuel] Buchweitz, R.O., Greuel, G.M., The Milnor number and deformations of complex curve singularities, Inventiones Math. 58 (1980), 241-281. Zbl0458.32014MR571575
  16. [Christophersen 1] Christophersen, J., Monomial curves and obstructions on cyclic quotient singularities, in 'Singularities, representations of algebras and vector bundles, Lambrecht 1985,' Lecture Notes in Mathematics1273, Springer Verlag, Berlin-Heidelberg- New York. Zbl0646.14001MR915170
  17. [Christophersen 2] Christopherson, J., 'Obstruction spaces for rational singularities and deformations of cyclic quotients,' Thesis, University of Oslo. 
  18. [Drewes] Drewes, R., 'Infinitesimale Deformationen von Kegeln über transkanonisch eingebetteten hyperelliptischen Kurven,' Diplomarbeit, Universität Hamburg, 1989. Zbl0736.14001MR1049900
  19. [Eagon-Northcott] Eagon, J.A., Northcott, D.C., Ideals defined by matrices and a certain complex associated with them, Proc. Royal Society London, Ser. A269 (1962), 188-204. Zbl0106.25603MR142592
  20. [Eisenbud] Eisenbud, D., Transcanonical embeddings of hyperelliptic curves, Jour. Pure Appl. Alg.19 (1980), 77-83. Zbl0444.14023MR593247
  21. [Eisenbud-Harris] Eisenbud, D., Harris, J., On varieties of minimal degree, Proc. of Symposia in Pure Math.46(1) (1987), 3-13. Zbl0646.14036
  22. [Fulton] Fulton, W., 'Intersection theory,' Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Bd. 2, Springer Verlag, Berlin -Heidelberg-New York. Zbl0541.14005MR1644323
  23. [Galligo] Galligo, A., Théorème de division et stabilité en géométrie analytique locale, Annales Institut Fourier29 (1979), 107-184. Zbl0412.32011MR539695
  24. [Gerstenhaber] Gerstenhaber, M., On the deformations of rings and algebras I, Annals of Math.79 (1964), 59-103. Zbl0123.03101MR171807
  25. [Greuel] Greuel, G.M., On deformations of curves and a formula of Deligne, in Algebraic Geometry, Proceedings, La Rabida1981, pp. 141-168. Zbl0509.14031MR708332
  26. [Greuel-Looijenga] Greuel, G.M., Looijenga, E., The dimension of smoothing components, Duke Math. Journal52 (1985), 263-272. Zbl0587.32038MR791301
  27. [Grauert] Grauert, H., Über die Deformationen isolierter Singularitäten analytischer Mengen, Inventiones Math.11 (1970), 263-292. Zbl0237.32011
  28. [Hironaka] Hironaka, On the arithmetic genera and the effective genera of algebraic curves, Mem. Coll. Sci. Univ. of Kyoto, Ser. A30 (1957), 177-195. Zbl0099.15702MR90850
  29. [Illusie] Illusie, L., 'Complexe cotangent et deformations I', Lecture Notes in Mathematics 239; —II, Lecture Notes in Mathematics289, Springer, Berlin -Heidelberg- New York. Zbl0238.13017
  30. [de Jong-van Straten] de Jong, Th., van Straten, D., Deformations of nonisolated singularities, in 'Nonisolated Hypersurface Singularities,' Thesis Th. de Jong, University of Nijmegen, 1988, pp. 71-158. 
  31. [Kahn] Kahn, C., Die infinitesimalen Deformationen der zweidimensionalen Quotientensingularitäten (nach Polyedergruppen), Diplomarbeit, Universität Hamburg, 1984. 
  32. [Kollár-Shepherd-Barron] Kollár, J., Shepherd-Barron, N.I., Threefolds and deformations of surface singularities, Inventiones Math.91 (1988), 299-338. Zbl0642.14008MR922803
  33. [Laudal] Laudal, O.A., Formal moduli of algebraic structures, Lecture Notes in Mathematics754, Springer-Verlag, Berlin-Heidelberg - New York. Zbl0438.14007MR551624
  34. [Laudal-Pfister] Laudal, O.A., Pfister, G., Local Moduli and Singularities, Lecture Notes in Mathematics1310, Springer-Verlag, Berlin- Heidelberg- New York. Zbl0657.14005MR950171
  35. [Laufer] Laufer, H., On minimally elliptic singularities, American Journal of Mathematics99 (1977), 1257-1295. Zbl0384.32003MR568898
  36. [Lichtenbaum-Schlessinger] Lichtenbaum, S., Schlessinger, M., The cotangent complex of a morphism, Transactions AMS128 (1967), 41-70. Zbl0156.27201MR209339
  37. [Morales] Morales, M., Calcul de quelques invariants des singularités de surfaces normales, Monographies Enseignements Math.31 (1983), 191-203, in 'Noeuds, Tresses et Singularités,' Proceedings Plans-Sur-Bex1982, ed. C. Weber. Zbl0542.14001MR728586
  38. [Mumford] Mumford, D., A remark on the paper of M. Schlessinger, Rice Univ. Studies59 (1973), 113-118. Zbl0279.32007MR347818
  39. [Pesselhoy-Riemenschneider] Pesselhoy, J., Riemenschneider, O., Projective resolutions of Hodge algebras. Some examples., Proceedings of Symposia in Pure Mathematics40 (1983), 305-317. Zbl0518.13005MR713257
  40. [Pinkham 1] Pinkham, H.C., Deformations of algebraic varieties with Gm action, Astérisque20 (1974). Zbl0304.14006
  41. [Pinkham 2] Pinkham, H.C., Deformations of cones with negative grading, Journal of Algebra30 (1974), 92-102. Zbl0284.14009MR347822
  42. [Pinkham 3] Pinkham, H.C., Normal surface singularities with C*-action, Math. Annalen227 (1977), 183-193. Zbl0331.14018MR432636
  43. [Pinkham 4] Pinkham, H.C., Deformations of quotient surface singularities, Proceedings of Symposia in Pure Mathematics30 (1977), 65-67. Zbl0365.14003MR447240
  44. [Reid] Reid, M., Canonical 3-folds, in Algebraic geometry, Proceedings, Angers1979, Sijthoff and Noordhoff, Alphen a.d. Rijn, pp. 273-310. Zbl0451.14014MR605348
  45. [Riemenschneider] Riemenschneider, O., Zweidimensionale Quotientensingularitäten: Gleichungen und Syzygien, Archiv der Math.37 (1981), 406-417. Zbl0456.14006MR643282
  46. [Rim] Rim, D.S., Formal deformation theory, in SGA 7, I, Lecture Notes in Mathematics288, Springer-Verlag, Berlin-Heidelberg - New York, 1972, pp. 32-132 Zbl0246.14001
  47. [Schlessinger 1] Schlessinger, M., Functors of Artin rings, Transactions AMS128 (1967), 41-70. MR217093
  48. [Schlessinger 2] Schlessinger, M., On rigid singularities, Rice University Studies59 (1973), 147-162. Zbl0279.32006MR344519
  49. [Stevens 1] Stevens, J., Kulikov singularities, Thesis, University of Leiden, 1985. 
  50. [Stevens 2] Stevens, J., On the number of points determining a canonical curve, Indagationes Math. (to appear). Zbl0724.14017MR1041502
  51. [Stevens 3] Stevens, J., On the versal deformation of cyclic quotient singularities, Preprint, Mathematisches Seminar der Universität Hamburg (1989). Zbl1315.14005MR1129040
  52. [van Straten] van Straten, D., Weakly normal surface singularities and their improvements, Thesis, Leiden1987. Zbl0638.14001
  53. [Svanes] Svanes, T., Coherent Cohomology on flag manifolds and rigidity, Thesis, MIT, Cambridge Mass., 1972. Zbl0308.14008
  54. [Tjurina] Tjurina, G.N., Locally semiuniversal flat deformations of isolated singularities of complex spaces, Math. USSR Izvestija3 (5) (1969), 967-999. Zbl0209.11301
  55. [Wahl 1] Wahl, J., Equisingular deformations of normal surface singularities I, Annals of Math.104 (1976), 325-356. Zbl0358.14007MR422270
  56. [Wahl 2] Wahl, J., Equations defining rational surface singularities, Ann. Sci. Ecole Normal Supérieure (1977), 231-264. Zbl0367.14004MR444655
  57. [Wahl 3] Wahl, J., Smoothings of normal surface singularities, Topology20 (1981), 219-246. Zbl0484.14012MR608599
  58. [Wahl 4] Wahl, J., The Jacobian algebra of a quasihomogeneous Gorenstein surface singularity, Duke Math. Journal55 (1987), 843-871. Zbl0644.14001MR916123
  59. [Wahl 5] Wahl, J., Deformations of quasihomogeneous surface singularities, Math. Ann.280 (1988), 105-128. Zbl0652.14001MR928300
  60. [Xambo] Xambo, S., On projective varieties of minimal degree, Collecteana Math.32 (1981), 149-164. Zbl0501.14020MR653892
  61. [Zariski] Zariski, O., Sur les modules des branches planes, Hermann, Paris. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.