Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2016_28_2_a6, author = {S. Yu. Orevkov and E. I. Shustin}, title = {Real algebraic and pseudoholomorphic curves on the quadratic cone and smoothings of singularity~$X_{21}$}, journal = {Algebra i analiz}, pages = {138--186}, publisher = {mathdoc}, volume = {28}, number = {2}, year = {2016}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2016_28_2_a6/} }
TY - JOUR AU - S. Yu. Orevkov AU - E. I. Shustin TI - Real algebraic and pseudoholomorphic curves on the quadratic cone and smoothings of singularity~$X_{21}$ JO - Algebra i analiz PY - 2016 SP - 138 EP - 186 VL - 28 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/AA_2016_28_2_a6/ LA - ru ID - AA_2016_28_2_a6 ER -
S. Yu. Orevkov; E. I. Shustin. Real algebraic and pseudoholomorphic curves on the quadratic cone and smoothings of singularity~$X_{21}$. Algebra i analiz, Tome 28 (2016) no. 2, pp. 138-186. http://geodesic.mathdoc.fr/item/AA_2016_28_2_a6/
[1] Akyol A., Degtyarev A., “Geography of irreducible plane sextics”, Proc. London Math. Soc. (3), 111 (2015), 1307–1337 | DOI | MR | Zbl
[2] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii, v. 1, Nauka, M., 1982 | MR
[3] Artal Bartolo E., Carmona Ruber J., Cogolludo Augustin J. I., “On sextic curves with big Milnor number”, Trend in Singularities, Trends Math., Birkhäuser, Basel, 2002, 1–29 | MR | Zbl
[4] Brugallé E., “Symmetric plane curves of degree 7: pseudoholomorphic and algebraic classifications”, J. Reine Angew. Math., 612 (2007), 129–171 | MR | Zbl
[5] Caporaso L., Harris J., “Parameter spaces for curves on surfaces and enumeration of rational curves”, Compositio Math., 113:2 (1998), 155–208 | DOI | MR | Zbl
[6] Degtyarev A., “On the Artal–Carmona–Cogolludo construction”, J. Knot Theory Ramifications, 23:5 (2014), 1450028, 35 pp. | DOI | MR | Zbl
[7] Dolgachev I. V., Classical algebraic geometry: a modern view, Cambridge Univ. Press, Cambridge, 2012 | MR | Zbl
[8] Fiedler-Le Touzé S., Orevkov S. Yu., “A flexible affine $M$-sextic which is algebraically unrealizable”, J. Algebraic Geom., 11:2 (2002), 293–310 | DOI | MR | Zbl
[9] Greuel G.-M., Karras U., “Families of varieties with prescribed singularities”, Compos. Math., 69:1 (1989), 83–110 | MR | Zbl
[10] Greuel G.-M., Lossen C., Shustin E., Introduction to singularities and deformations, Springer Monogr. Math., Springer, Berlin, 2007 | MR | Zbl
[11] Gudkov D. A., Utkin G. A., Tai M. L., “Polnaya klassifikatsiya neraspadayuschikhsya krivykh $4$-go poryadka”, Mat. sb., 69(111):2 (1966), 222–256 | MR | Zbl
[12] Gudkov D. A., Shustin E. I., “On the intersection of the close algebraic curves”, Topology (Leningrad, 1982), Lecture Notes in Math., 1060, Springer, Berlin, 1984, 278–289 | DOI | MR
[13] Kharlamov E. I., Orevkov S. Yu., Shustin E. I., “Singularity which has no $M$-smoothing”, The Arnoldfest (Toronto, ON, 1997), Fields Inst. Commun., 24, Amer. Math. Soc., Providence, RI, 1999, 273–309 | MR | Zbl
[14] Kharlamov V. M., Viro O. Ya., “Extensions of the Gudkov–Rokhlin congruence”, Topology and Geometry Rohlin Semin., Lecture Notes in Math., 1346, Springer, Berlin, 1988, 357–406 | DOI | MR
[15] Korchagin A. B., “Novye $M$-krivye stepeni 8 i 9”, Dokl. AN SSSR, 39:3 (1989), 569–572 | MR | Zbl
[16] Korchagin A. B., “Construction of new curves of $9$th degree”, Real Algebraic Geometry (Rennes, 1991), Lecture Notes in Math., 1524, Springer, Berlin, 1992, 296–307 | DOI | MR
[17] Korchagin A. B., Shustin E. I., “Affinnye krivye stepeni $6$ i ustraneniya nevyrozhdennoi shestikratnoi osoboi tochki”, Izv. AN SSSR. Ser. mat., 52:6 (1988), 1181–1199 | MR | Zbl
[18] Moody E. I., “Notes on the Bertini involution”, Bull. Amer. Math. Soc., 49 (1943), 433–436 | DOI | MR | Zbl
[19] Orevkov S. Yu., “Classification of flexible $M$-curves of degree $8$ up to isotopy”, Geom. Funct. Anal., 12:4 (2002), 723–755 | DOI | MR | Zbl
[20] Orevkov S. Yu., “Postroeniya raspolozhenii $M$-kvartiki i $M$-kubiki s maksimalno peresekayuschimisya ovalom i nechetnoi vetvyu”, Vestn. Nizhegorod. gos. un-ta. Ser. mat. model., optim. uprav., 2002, no. 1, 12–48
[21] Orevkov S. Yu., “Riemann existence theorem and construction of real algebraic curves”, Ann. Fac. Sci. de Toulouse. Math. (6), 12:4 (2003), 517–531 | DOI | MR | Zbl
[22] Orevkov S. Yu., “Quasipositivity problem for $3$-braids”, Turkish J. Math., 28:1 (2004), 89–93 | MR | Zbl
[23] Orevkov S. Yu., “Raspolozheniya $M$-kvintiki otnositelno koniki, maksimalno peresekayuschei ee nechetnuyu vetv”, Algebra i analiz, 19:4 (2007), 174–242 | MR | Zbl
[24] Orevkov S. Yu., “Algorithmic recognition of quasipositive braids of algebraic length two”, J. Algebra, 423 (2015), 1080–1108 | DOI | MR | Zbl
[25] Orevkov S. Yu., Shustin E. I., “Flexible, algebraically unrealizable curves: rehabilitation of the Hilbert–Rohn–Gudkov approach”, J. Reine Angew. Math., 551 (2002), 145–172 | MR | Zbl
[26] Orevkov S. Yu., Shustin E. I., “Pseudoholomorphic, algebraically unrealizable curves”, Mosc. Math. J., 3:3 (2003), 1053–1083 | MR | Zbl
[27] Risler J.-J., “Un analogue local du théorème de Harnack”, Invent. Math., 89:1 (1987), 119–137 | DOI | MR | Zbl
[28] Shustin E. I., “Metod Gilberta–Roona i sglazhivaniya osobykh tochek veschestvennykh algebraicheskikh krivykh”, Dokl. AN SSSR, 281:1 (1983), 33–36 | MR
[29] Shustin E. I., “Versalnye deformatsii v prostranstve ploskikh krivykh fiksirovannoi stepeni”, Funkts. anal. i ego pril., 21:1 (1985), 90–91 | MR | Zbl
[30] Shustin E., “Gluing of singular and critical points”, Topology, 37:1 (1998), 195–217 | DOI | MR | Zbl
[31] Viro O., Patchworking real algebraic varieties, Preprint, arXiv: math/0611382[math.AG]
[32] Viro O. Ya., “Ploskie veschestvennye algebraicheskie krivye: postroeniya s kontroliruemoi topologiei”, Algebra i analiz, 1:5 (1989), 1–73 | MR | Zbl
[33] Welschinger J.-Y., “Courbes algébriques réelles et courbes flexibles sur les surfaces réglées de base $\mathbb CP^1$”, Proc. London Math. Soc. (3), 85:2 (2002), 367–392 | DOI | MR | Zbl
[34] Van der Waerden B. L., Einfürung in die algebraische Geometrie, 2nd ed., Springer, 1974