Hypersurface sections and obstructions (rational surface singularities)

Behnke, Kurt; Christophersen, Jan Arthur

Behnke, Kurt ; Christophersen, Jan Arthur

Compositio Mathematica, Tome 77 (1991) no. 3, pp. 233-268.

MR Zbl

@article{CM_1991__77_3_233_0,
     author = {Behnke, Kurt and Christophersen, Jan Arthur},
     title = {Hypersurface sections and obstructions (rational surface singularities)},
     journal = {Compositio Mathematica},
     pages = {233--268},
     publisher = {Kluwer Academic Publishers},
     volume = {77},
     number = {3},
     year = {1991},
     mrnumber = {1092769},
     zbl = {0728.14034},
     language = {en},
     url = {http://www.numdam.org/item/CM_1991__77_3_233_0/}
}

TY  - JOUR
AU  - Behnke, Kurt
AU  - Christophersen, Jan Arthur
TI  - Hypersurface sections and obstructions (rational surface singularities)
JO  - Compositio Mathematica
PY  - 1991
SP  - 233
EP  - 268
VL  - 77
IS  - 3
PB  - Kluwer Academic Publishers
UR  - http://www.numdam.org/item/CM_1991__77_3_233_0/
LA  - en
ID  - CM_1991__77_3_233_0
ER  -

%0 Journal Article
%A Behnke, Kurt
%A Christophersen, Jan Arthur
%T Hypersurface sections and obstructions (rational surface singularities)
%J Compositio Mathematica
%D 1991
%P 233-268
%V 77
%N 3
%I Kluwer Academic Publishers
%U http://www.numdam.org/item/CM_1991__77_3_233_0/
%G en
%F CM_1991__77_3_233_0

Behnke, Kurt; Christophersen, Jan Arthur. Hypersurface sections and obstructions (rational surface singularities). Compositio Mathematica, Tome 77 (1991) no. 3, pp. 233-268. http://www.numdam.org/item/CM_1991__77_3_233_0/

Bibliographie
Cité par

1 Oscar Zariski, Studies in equisingularity I. Equivalent singularities of plane algebroid curves, Amer. J. Math. 87 (1965), 507-536. | MR | Zbl

[Aleksandrov] Aleksandrov, A.G., On deformations of one-dimensional singularities with c = δ + 1, Russian Math. Surveys 33:3 (1978), 139-140. | Zbl

[André] André, M., Homologie des algèbres commutatives, Grundlehren der mathematischen Wissenschaften, Bd. 206, Springer, Berlin- Heidelberg-New York. | MR | Zbl

[Arndt] Arndt, J., Verselle Deformationen zyklischer Quotientensingularitäten, Dissertation, Universität Hamburg, 1988. | Zbl

[Artin 1] Artin, M., On isolated rational singularities of surfaces, American Journal of Math. 88 (1966), 129-136. | MR | Zbl

[Artin 2] Artin, M., Deformations of singularities, Tata Lecture Notes.

[Artin-Verdier] Artin, M., Verdier, J.L., Reflexive modules over rational double points, Math. Ann. 270 (1985), 79-82. | EuDML | MR | Zbl

[Bayer-Christophersen] Bayer, D., Christophersen, J.A., In preparation.

[Behnke] Behnke, K., Infinitesimal deformations of cusp singularities, Math. Annalen 265 (1983), 407-422. | EuDML | MR | Zbl

[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. | MR | Zbl

[Behnke-Knörrer] Behnke, K., Knörrer, H., On the infinitesimal deformations of rational surface singularities, Compositio Math. 61 (1987), 103-127. | Numdam | MR | Zbl

[Brieskorn] Brieskorn, E., Rationale Singularitäten komplexer Flächen, Inventiones Math. 4 (1968), 336-358. | MR | Zbl

[Brieskorn-Knörrer] Brieskorn, E., Knörrer, H., Ebene Algebraische Kurven, Birkhäuser, Basel. | MR | Zbl

[Buchweitz] Buchweitz, R.O., Deformations de diagrammes, deploiments et singularités très rigides, liaison algébrique, Thèses présentées à l'Université Paris VII, 1981.

[Buchweitz-Greuel] Buchweitz, R.O., Greuel, G.M., The Milnor number and deformations of complex curve singularities, Inventiones Math. 58 (1980), 241-281. | MR | Zbl

[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 Mathematics 1273, Springer Verlag, Berlin-Heidelberg- New York. | MR | Zbl

[Christophersen 2] Christopherson, J., 'Obstruction spaces for rational singularities and deformations of cyclic quotients,' Thesis, University of Oslo.

[Drewes] Drewes, R., 'Infinitesimale Deformationen von Kegeln über transkanonisch eingebetteten hyperelliptischen Kurven,' Diplomarbeit, Universität Hamburg, 1989. | MR | Zbl

[Eagon-Northcott] Eagon, J.A., Northcott, D.C., Ideals defined by matrices and a certain complex associated with them, Proc. Royal Society London, Ser. A 269 (1962), 188-204. | MR | Zbl

[Eisenbud] Eisenbud, D., Transcanonical embeddings of hyperelliptic curves, Jour. Pure Appl. Alg. 19 (1980), 77-83. | MR | Zbl

[Eisenbud-Harris] Eisenbud, D., Harris, J., On varieties of minimal degree, Proc. of Symposia in Pure Math. 46(1) (1987), 3-13. | Zbl

[Fulton] Fulton, W., 'Intersection theory,' Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Bd. 2, Springer Verlag, Berlin -Heidelberg-New York. | MR | Zbl

[Galligo] Galligo, A., Théorème de division et stabilité en géométrie analytique locale, Annales Institut Fourier 29 (1979), 107-184. | Numdam | MR | Zbl

[Gerstenhaber] Gerstenhaber, M., On the deformations of rings and algebras I, Annals of Math. 79 (1964), 59-103. | MR | Zbl

[Greuel] Greuel, G.M., On deformations of curves and a formula of Deligne, in Algebraic Geometry, Proceedings, La Rabida 1981, pp. 141-168. | MR | Zbl

[Greuel-Looijenga] Greuel, G.M., Looijenga, E., The dimension of smoothing components, Duke Math. Journal 52 (1985), 263-272. | MR | Zbl

[Grauert] Grauert, H., Über die Deformationen isolierter Singularitäten analytischer Mengen, Inventiones Math. 11 (1970), 263-292. | Zbl

[Hironaka] Hironaka, On the arithmetic genera and the effective genera of algebraic curves, Mem. Coll. Sci. Univ. of Kyoto, Ser. A 30 (1957), 177-195. | MR | Zbl

[Illusie] Illusie, L., 'Complexe cotangent et deformations I', Lecture Notes in Mathematics 239; -II, Lecture Notes in Mathematics 289, Springer, Berlin -Heidelberg- New York. | Zbl

[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.

[Kahn] Kahn, C., Die infinitesimalen Deformationen der zweidimensionalen Quotientensingularitäten (nach Polyedergruppen), Diplomarbeit, Universität Hamburg, 1984.

[Kollár-Shepherd-Barron] Kollár, J., Shepherd-Barron, N.I., Threefolds and deformations of surface singularities, Inventiones Math. 91 (1988), 299-338. | MR | Zbl

[Laudal] Laudal, O.A., Formal moduli of algebraic structures, Lecture Notes in Mathematics 754, Springer-Verlag, Berlin-Heidelberg - New York. | MR | Zbl

[Laudal-Pfister] Laudal, O.A., Pfister, G., Local Moduli and Singularities, Lecture Notes in Mathematics 1310, Springer-Verlag, Berlin- Heidelberg- New York. | MR | Zbl

[Laufer] Laufer, H., On minimally elliptic singularities, American Journal of Mathematics 99 (1977), 1257-1295. | MR | Zbl

[Lichtenbaum-Schlessinger] Lichtenbaum, S., Schlessinger, M., The cotangent complex of a morphism, Transactions AMS 128 (1967), 41-70. | MR | Zbl

[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-Bex 1982, ed. C. Weber. | MR | Zbl

[Mumford] Mumford, D., A remark on the paper of M. Schlessinger, Rice Univ. Studies 59 (1973), 113-118. | MR | Zbl

[Pesselhoy-Riemenschneider] Pesselhoy, J., Riemenschneider, O., Projective resolutions of Hodge algebras. Some examples., Proceedings of Symposia in Pure Mathematics 40 (1983), 305-317. | MR | Zbl

[Pinkham 1] Pinkham, H.C., Deformations of algebraic varieties with Gm action, Astérisque 20 (1974). | Numdam | Zbl

[Pinkham 2] Pinkham, H.C., Deformations of cones with negative grading, Journal of Algebra 30 (1974), 92-102. | MR | Zbl

[Pinkham 3] Pinkham, H.C., Normal surface singularities with C*-action, Math. Annalen 227 (1977), 183-193. | MR | Zbl

[Pinkham 4] Pinkham, H.C., Deformations of quotient surface singularities, Proceedings of Symposia in Pure Mathematics 30 (1977), 65-67. | MR | Zbl

[Reid] Reid, M., Canonical 3-folds, in Algebraic geometry, Proceedings, Angers 1979, Sijthoff and Noordhoff, Alphen a.d. Rijn, pp. 273-310. | MR | Zbl

[Riemenschneider] Riemenschneider, O., Zweidimensionale Quotientensingularitäten: Gleichungen und Syzygien, Archiv der Math. 37 (1981), 406-417. | MR | Zbl

[Rim] Rim, D.S., Formal deformation theory, in SGA 7, I, Lecture Notes in Mathematics 288, Springer-Verlag, Berlin-Heidelberg - New York, 1972, pp. 32-132 | Zbl

[Schlessinger 1] Schlessinger, M., Functors of Artin rings, Transactions AMS 128 (1967), 41-70. | MR

[Schlessinger 2] Schlessinger, M., On rigid singularities, Rice University Studies 59 (1973), 147-162. | MR | Zbl

[Stevens 1] Stevens, J., Kulikov singularities, Thesis, University of Leiden, 1985.

[Stevens 2] Stevens, J., On the number of points determining a canonical curve, Indagationes Math. (to appear). | MR | Zbl

[Stevens 3] Stevens, J., On the versal deformation of cyclic quotient singularities, Preprint, Mathematisches Seminar der Universität Hamburg (1989). | MR

[van Straten] Van Straten, D., Weakly normal surface singularities and their improvements, Thesis, Leiden 1987.

[Svanes] Svanes, T., Coherent Cohomology on flag manifolds and rigidity, Thesis, MIT, Cambridge Mass., 1972.

[Tjurina] Tjurina, G.N., Locally semiuniversal flat deformations of isolated singularities of complex spaces, Math. USSR Izvestija 3 (5) (1969), 967-999. | Zbl

[Wahl 1] Wahl, J., Equisingular deformations of normal surface singularities I, Annals of Math. 104 (1976), 325-356. | MR | Zbl

[Wahl 2] Wahl, J., Equations defining rational surface singularities, Ann. Sci. Ecole Normal Supérieure (1977), 231-264. | Numdam | MR | Zbl

[Wahl 3] Wahl, J., Smoothings of normal surface singularities, Topology 20 (1981), 219-246. | MR | Zbl

[Wahl 4] Wahl, J., The Jacobian algebra of a quasihomogeneous Gorenstein surface singularity, Duke Math. Journal 55 (1987), 843-871. | MR | Zbl

[Wahl 5] Wahl, J., Deformations of quasihomogeneous surface singularities, Math. Ann. 280 (1988), 105-128. | MR | Zbl

[Xambo] Xambo, S., On projective varieties of minimal degree, Collecteana Math. 32 (1981), 149-164. | MR | Zbl

[Zariski] Zariski, O., Sur les modules des branches planes, Hermann, Paris.