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Uspekhi Mat. Nauk, 2000, Volume 55, Issue 4(334), Pages 129–212 (Mi umn315)  

This article is cited in 55 scientific papers (total in 55 papers)

Topological properties of real algebraic varieties: du coté de chez Rokhlin

A. I. Degtyareva, V. M. Kharlamovb

a Bilkent University
b University Louis Pasteur

Abstract: The survey covers results in the topology of real algebraic varieties in the direction initiated in the early seventies by V. I. Arnol'd and V. A. Rokhlin. We make an attempt to systematize the principal achievements in the subject. After presenting general tools and results, we pay special attention to surfaces and curves on surfaces.

DOI: https://doi.org/10.4213/rm315

Full text: PDF file (819 kB)
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English version:
Russian Mathematical Surveys, 2000, 55:4, 735–814

Bibliographic databases:

UDC: 515.165.4
MSC: 14P25, 14J99, 57S25
Received: 09.12.1999

Citation: A. I. Degtyarev, V. M. Kharlamov, “Topological properties of real algebraic varieties: du coté de chez Rokhlin”, Uspekhi Mat. Nauk, 55:4(334) (2000), 129–212; Russian Math. Surveys, 55:4 (2000), 735–814

Citation in format AMSBIB
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    1. Orevkov S.Yu., “Real quintic surface with 23 components”, C. R. Acad. Sci. Paris Sér. I Math., 333:2 (2001), 115–118  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    2. Degtyarev A., Kharlamov V., “Real rational surfaces are quasi-simple”, J. Reine Angew. Math., 2002:551 (2002), 87–99  crossref  mathscinet  zmath  isi  elib
    3. Vik. S. Kulikov, V. M. Kharlamov, “On real structures on rigid surfaces”, Izv. Math., 66:1 (2002), 133–150  mathnet  crossref  crossref  mathscinet  zmath
    4. Welschinger J.-Y., “Forme d'intersection tordue et extension de la congruence d'Arnol'd [Twisted intersection form and extension of the Arnolʹd congruence]”, Math. Z., 242:3 (2002), 589–614  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Welschinger J.-Y., “Courbes algébriques réelles et courbes flexibles sur les surfaces réglées de base $\mathbb C\roman P^1$ [Real algebraic curves and flexible curves on ruled surfaces of base $\mathbb C\roman P^1$]”, Proc. London Math. Soc. (3), 85:2 (2002), 367–392  crossref  mathscinet  zmath  isi  scopus  scopus
    6. I. O. Kalinin, “On the cohomology of real algebraic varieties”, J. Math. Sci. (N. Y.), 131:1 (2005), 5323–5344  mathnet  crossref  mathscinet  zmath  elib
    7. Itenberg I., Kharlamov V., Shustin E., “Welschinger invariant and enumeration of real rational curves”, Int. Math. Res. Not., 2003, no. 49, 2639–2653  crossref  mathscinet  zmath  isi  elib
    8. Itenberg I., Shustin E., “Critical points of real polynomials and topology of real algebraic $T$-surfaces”, Geom. Dedicata, 101:1 (2003), 61–91  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Bihan F., “Asymptotic behaviour of Betti numbers of real algebraic surfaces”, Comment. Math. Helv., 78:2 (2003), 227–244  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. Welschinger J.-Y., “Real structures on minimal ruled surfaces”, Comment. Math. Helv., 78:2 (2003), 418–446  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. Itenberg I., Shustin E., “Viro theorem and topology of real and complex combinatorial hypersurfaces”, Israel J. Math., 133 (2003), 189–238  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. Welschinger J.-Y., “Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry”, C. R. Math. Acad. Sci. Paris, 336:4 (2003), 341–344  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Catanese F., Frediani P., “Real Hyperelliptic Surfaces and the Orbifold Fundamental Group”, J. Inst. Math. Jussieu, 2:2 (2003), 169–233  crossref  mathscinet  isi  scopus  scopus
    14. Itenberg I., “Amibes de variétés algébriques et dénombrement de courbes (d'après G. Mikhalkin) [Amoebas of algebraic varieties and enumeration of curves (following G. Mikhalkin)]”, Astérisque, 294, 2004, 335–361  mathscinet  zmath  isi
    15. Degtyarev A., Itenberg I., Kharlamov V., “Finiteness and quasi-simplicity for symmetric $K3$-surfaces”, Duke Math. J., 122:1 (2004), 1–49  crossref  mathscinet  zmath  isi  scopus  scopus
    16. Welschinger J.-Y., “Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry”, Invent. Math., 162:1 (2005), 195–234  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    17. V. B. Demidovich, G. G. Magaril-Il'yaev, V. M. Tikhomirov, “Extremal problems for linear functionals on the Tchebycheff spaces”, J. Math. Sci., 142:2 (2007), 1923–1932  mathnet  crossref  mathscinet  zmath  elib  elib
    18. Florens V., “Signatures of colored links with application to real algebraic curves”, J. Knot Theory Ramifications, 14:7 (2005), 883–918  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    19. Öztürk F., “Generalised Thurston-Bennequin invariants for real algebraic surface singularities”, Manuscripta Math., 117:3 (2005), 273–298  crossref  mathscinet  zmath  isi  scopus  scopus
    20. Soprunova E., Sottile F., “Lower bounds for real solutions to sparse polynomial systems”, Adv. Math., 204:1 (2006), 116–151  crossref  mathscinet  zmath  isi  scopus
    21. Laszlo Y., Viterbo C., “Estimates of characteristic numbers of real algebraic varieties”, Topology, 45:2 (2006), 261–280  crossref  mathscinet  zmath  isi  scopus  scopus
    22. Dimca A., “Singularities and their deformations: how they change the shape and view of objects”, Algebraic Geometry and Geometric Modeling, Mathematics and Visualization, 2006, 87–101  crossref  mathscinet  zmath  isi  scopus  scopus
    23. Kharlamov V., “Overview of topological properties of real algebraic surfaces”, Algebraic Geometry and Geometric Modeling, Mathematics and Visualization, 2006, 103–117  crossref  mathscinet  zmath  isi  scopus  scopus
    24. Brugallé E., “Symmetric plane curves of degree 7: pseudoholomorphic and algebraic classifications”, J. Reine Angew. Math., 2007:612 (2007), 129–171  crossref  mathscinet  zmath  isi  elib  scopus
    25. S. Yu. Orevkov, “Arrangements of an $M$-quintic with respect to a conic that maximally intersects its odd branch”, St. Petersburg Math. J., 19:4 (2008), 625–674  mathnet  crossref  mathscinet  zmath  isi  elib
    26. V. A. Krasnov, “Real algebraic varieties and cobordism”, Izv. Math., 71:3 (2007), 573–601  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    27. Proc. Steklov Inst. Math., 258 (2007), 178–193  mathnet  crossref  mathscinet  zmath  elib
    28. Bihan F., Mangolte F., “Topological types of real regular Jacobian elliptic surfaces”, Geom. Dedicata, 127:1 (2007), 57–73  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    29. Fiedler-Le Touzé S., “Pencils of cubics as tools to solve an interpolation problem”, Appl. Algebra Engrg. Comm. Comput., 18:1-2 (2007), 53–70  crossref  mathscinet  zmath  isi  scopus  scopus
    30. Teh Jyh-Haur, “Harnack-Thom theorem for higher cycle groups and picard varieties”, Trans. Amer. Math. Soc., 360:6 (2008), 3263–3285  crossref  mathscinet  zmath  isi  scopus  scopus
    31. Degtyarev A., “On deformations of singular plane sextics”, J. Algebraic Geom., 17:1 (2008), 101–135  crossref  mathscinet  zmath  isi  scopus  scopus
    32. Breske S., Labs O., van Straten D., “Real line arrangements and surfaces with many real nodes”, Geometric Modeling and Algebraic Geometry, 2008, 47–54  crossref  mathscinet  zmath  isi  scopus  scopus
    33. Brugallé E., Labs O., “Surfaces with many solitary points”, Geom. Dedicata, 141 (2009), 123–135  crossref  mathscinet  zmath  isi  scopus  scopus
    34. S. Yu. Nemirovski, “Homology class of a Lagrangian Klein bottle”, Izv. Math., 73:4 (2009), 689–698  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    35. “Introduction to tropical geometry”, Tropical Algebraic Geometry, Oberwolfach Seminars, 35, 2009, 1  mathscinet  isi
    36. V. A. Krasnov, “Real three-dimensional biquadrics”, Izv. Math., 74:4 (2010), 781–804  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    37. Finashin S., Kharlamov V., “Topology of real cubic fourfolds”, Journal of Topology, 3:1 (2010), 1–28  crossref  mathscinet  zmath  isi  scopus  scopus
    38. Azar M., Gabrielov A., “Some Lower Bounds in the B. and M. Shapiro Conjecture for Flag Varieties”, Discrete & Computational Geometry, 46:4 (2011), 636–659  crossref  mathscinet  zmath  isi  scopus  scopus
    39. Smirani M., Akriche M., “Real Elliptic Surfaces with Double Section and Real Tetragonal Curves”, Bull. Belg. Math. Soc.-Simon Steven, 19:3 (2012), 445–460  mathscinet  zmath  isi
    40. Lanzat S., Polyak M., “Counting Real Curves with Passage/Tangency Conditions”, J. Lond. Math. Soc.-Second Ser., 85:Part 3 (2012), 838–854  crossref  mathscinet  zmath  isi  scopus  scopus
    41. I. Itenberg, G. Mikhalkin, “On Block-Gottsche Multiplicities for Planar Tropical Curves”, International Mathematics Research Notices, 2012  crossref  mathscinet  isi  scopus  scopus
    42. Oancea A., “Welschinger's Invariants”, Asterisque, 2012, no. 348, 265–297  mathscinet  zmath  isi
    43. Soprunova E., Sottile F., “Lower Bounds in Real Algebraic Geometry and Orientability of Real Toric Varieties”, Discret. Comput. Geom., 50:2 (2013), 509–519  crossref  mathscinet  zmath  isi  scopus  scopus
    44. Brugalle E., Puignau N., “Enumeration of Real Conics and Maximal Configurations”, J. Eur. Math. Soc., 15:6 (2013), 2139–2164  crossref  mathscinet  zmath  isi  scopus  scopus
    45. Lothar Göttsche, Vivek Shende, “Refined curve counting on complex surfaces”, Geom. Topol, 18:4 (2014), 2245  crossref  mathscinet  zmath  isi  scopus  scopus
    46. Okonek Ch., Teleman A., “A Wall-Crossing Formula For Degrees of Real Central Projections”, Int. J. Math., 25:4 (2014), 14500384  crossref  mathscinet  isi  scopus  scopus
    47. Okonek Ch., Teleman A., “Intrinsic Signs and Lower Bounds in Real Algebraic Geometry”, J. Reine Angew. Math., 688 (2014), 219–241  crossref  mathscinet  zmath  isi  scopus  scopus
    48. Erwan Brugallé, “Floor diagrams relative to a conic, and GW–W invariants of Del Pezzo surfaces”, Advances in Mathematics, 279 (2015), 438  crossref  mathscinet  zmath  isi  scopus  scopus
    49. Renaudineau A., “a Real Sextic Surface With 45 Handles”, Math. Z., 281:1-2 (2015), 241–256  crossref  mathscinet  zmath  isi  scopus  scopus
    50. Rieken S., “Moduli of real pointed quartic curves”, Geod. Dedic., 185:1 (2016), 171–203  crossref  mathscinet  zmath  isi  scopus
    51. D'Mello Sh., “Classification of real rational knots of low degree in the 3-sphere”, J. Knot Theory Ramifications, 26:4 (2017), 1750020  crossref  mathscinet  zmath  isi  scopus
    52. Kharlamov V., Rasdeaconu R., “Qualitative aspects of counting real rational curves on real K3 surfaces”, Geom. Topol., 21:1 (2017), 585–601  crossref  mathscinet  zmath  isi  scopus
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    55. Brugalle E., “Surgery of Real Symplectic Fourfolds and Welschinger Invariants”, J. Singul., 17 (2018), 267–294  crossref  mathscinet  zmath  isi  scopus
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