We prove that for a Q-Gorenstein degeneration of del Pezzo surfaces, the number of non-Du Val singularities is at most . Degenerations with and non-Du Val points are investigated
Nous montrons que pour une dégénérescence Q-Gorenstein de surfaces de del Pezzo, le nombre de singularités non-Du Val est au plus . Les dégénérescences avec et points non-Du Val sont étudiées.
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.2934
Classification: 14J10, 14E30
Keywords: del Pezzo surface, T-singularity, deformation
@article{AIF_2015__65_1_369_0, author = {Prokhorov, Yuri}, title = {A note on degenerations of del {Pezzo} surfaces}, journal = {Annales de l'Institut Fourier}, pages = {369--388}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {65}, number = {1}, year = {2015}, doi = {10.5802/aif.2934}, zbl = {06496543}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2934/} }
TY - JOUR TI - A note on degenerations of del Pezzo surfaces JO - Annales de l'Institut Fourier PY - 2015 DA - 2015/// SP - 369 EP - 388 VL - 65 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2934/ UR - https://zbmath.org/?q=an%3A06496543 UR - https://doi.org/10.5802/aif.2934 DO - 10.5802/aif.2934 LA - en ID - AIF_2015__65_1_369_0 ER -
Prokhorov, Yuri. A note on degenerations of del Pezzo surfaces. Annales de l'Institut Fourier, Volume 65 (2015) no. 1, pp. 369-388. doi : 10.5802/aif.2934. https://aif.centre-mersenne.org/articles/10.5802/aif.2934/
[1] Rationale Singularitäten komplexer Flächen, Invent. Math., Tome 4 (1967/1968), pp. 336-358 | Article | MR: 222084 | Zbl: 0219.14003
[2] Fifteen characterizations of rational double points and simple critical points, Enseign. Math. (2), Tome 25 (1979) no. 1-2, pp. 131-163 | MR: 543555 | Zbl: 0418.14020
[3] Compact moduli of plane curves, Duke Math. J., Tome 124 (2004) no. 2, pp. 213-257 | Article | MR: 2078368 | Zbl: 1060.14034
[4] Compact moduli spaces of surfaces of general type, Compact moduli spaces and vector bundles (Contemp. Math.) Tome 564, Amer. Math. Soc., Providence, RI, 2012, pp. 1-18 | Article | MR: 2895182 | Zbl: 1254.14043
[5] Exceptional bundles associated to degenerations of surfaces, Duke Math. J., Tome 162 (2013) no. 6, pp. 1171-1202 | Article | MR: 3053568 | Zbl: 1282.14074
[6] Smoothable del Pezzo surfaces with quotient singularities, Compos. Math., Tome 146 (2010) no. 1, pp. 169-192 | Article | MR: 2581246 | Zbl: 1194.14054
[7] Three-block exceptional sets on del Pezzo surfaces, Izv. Ross. Akad. Nauk Ser. Mat., Tome 62 (1998) no. 3, pp. 3-38 | Article | MR: 1642152 | Zbl: 0949.14026
[8] Threefolds and deformations of surface singularities, Invent. Math., Tome 91 (1988) no. 2, pp. 299-338 | Article | MR: 922803 | Zbl: 0642.14008
[9] Flips and abundance for algebraic threefolds (Kollár, János, ed.), Société Mathématique de France, Paris, 1992, pp. 1-258 (Papers from the Second Summer Seminar on Algebraic Geometry held at the University of Utah, Salt Lake City, Utah, August 1991, Astérisque No. 211 (1992)) | MR: 1225842
[10] Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, Tome 134, Cambridge University Press, Cambridge, 1998, viii+254 pages (With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original) | Article | MR: 1658959 | Zbl: 0926.14003
[11] Normal degenerations of the complex projective plane, J. Reine Angew. Math., Tome 419 (1991), pp. 89-118 | Article | MR: 1116920 | Zbl: 0719.14023
[12] Gorenstein log del Pezzo surfaces of rank one, J. Algebra, Tome 118 (1988) no. 1, pp. 63-84 | Article | MR: 961326 | Zbl: 0664.14019
[13] The birational geometry of surfaces with rational double points, Math. Ann., Tome 271 (1985) no. 3, pp. 415-438 | Article | MR: 787190 | Zbl: 0539.14008
[14] On semistable Mori contractions, Izv. Ross. Akad. Nauk Ser. Mat., Tome 68 (2004) no. 2, pp. 147-158 | Article | MR: 2058003 | Zbl: 1075.14014
[15] Towards the second main theorem on complements, J. Algebraic Geom., Tome 18 (2009) no. 1, pp. 151-199 | Article | MR: 2448282 | Zbl: 1159.14020
[16] Lectures on complements on log surfaces, MSJ Memoirs, Tome 10, Mathematical Society of Japan, Tokyo, 2001, viii+130 pages | MR: 1830440 | Zbl: 1037.14003
[17] Young person’s guide to canonical singularities, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) (Proc. Sympos. Pure Math.) Tome 46, Amer. Math. Soc., Providence, RI, 1987, pp. 345-414 | MR: 927963 | Zbl: 0634.14003
[18] Complements on surfaces, J. Math. Sci. (New York), Tome 102 (2000) no. 2, pp. 3876-3932 (Algebraic geometry, 10) | Article | MR: 1794169 | Zbl: 1177.14078
[19] Smoothings of normal surface singularities, Topology, Tome 20 (1981) no. 3, pp. 219-246 | Article | MR: 608599 | Zbl: 0484.14012
Cited by Sources: