Morphisms, line bundles and moduli spaces in real algebraic geometry
Publications Mathématiques de l'IHÉS, Volume 86 (1997), p. 5-65
@article{PMIHES_1997__86__5_0,
     author = {Bochnak, Jacek and Kucharz, Wojciech and Silhol, Robert},
     title = {Morphisms, line bundles and moduli spaces in real algebraic geometry},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {86},
     year = {1997},
     pages = {5-65},
     zbl = {0938.14033},
     mrnumber = {99h:14055},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1997__86__5_0}
}
Morphisms, line bundles and moduli spaces in real algebraic geometry. Publications Mathématiques de l'IHÉS, Volume 86 (1997) pp. 5-65. http://www.numdam.org/item/PMIHES_1997__86__5_0/

[1] J. Bochnak, M. Coste and M.-F. Roy, Géométrie Algébrique Réelle, Ergeb. Math., vol. 12, Springer-Verlag, 1987. | MR 90b:14030 | Zbl 0633.14016

[2] J. Bochnak and W. Kucharz, Algebraic approximation of mappings into spheres, Michigan Math. J., 34 (1987), 119-125. | MR 88h:58018 | Zbl 0631.14019

[3] J. Bochnak and W. Kucharz, Representation of homotopy classes by algebraic mappings, J. Reine Angew. Math. 377 (1987), 159-169. | MR 88g:14016 | Zbl 0619.14014

[4] J. Bochnak and W. Kucharz, On real algebraic morphisms into even-dimensional spheres, Ann. of Math. 128 (1988), 415-433. | MR 89k:57060 | Zbl 0674.14013

[5] J. Bochnak and W. Kucharz, Algebraic models of smooth manifolds, Invent. Math. 97 (1989), 585-611. | MR 91b:14076 | Zbl 0687.14023

[6] J. Bochnak and W. Kucharz, Nonisomorphic algebraic models of a smooth manifold, Math. Ann. 290 (1991), 1-2. | MR 92c:14053 | Zbl 0714.14012

[7] J. Bochnak and W. Kucharz, Vector bundles on a product of real cubic curves, K-Theory (1992) 487-497. | MR 94e:14077 | Zbl 0782.14014

[8] J. Bochnak and W. Kucharz, Complex cycles on real algebraic models of a smooth manifold, Proc. Amer. Math. Soc. 114 (1992), 1097-1104. | MR 93g:57032 | Zbl 0760.57011

[9] J. Bochnak and W. Kucharz, Elliptic curves and real algebraic morphisms, J. Algebraic Geometry 2 (1993), 635-666. | MR 94e:14072 | Zbl 0807.14046

[10] J. Bochnak, M. Buchner and W. Kucharz, Vector bundles over real algebraic varieties, K-Theory 3 (1989), 271-298. Erratum, K-Theory 4 (1990), p. 103. | MR 91b:14075 | Zbl 0761.14020

[11] P. Deligne, Le théorème de Noether, in : SGA 7II, p. 328-340, Lecture Notes in Math. 340, Springer, 1973. | MR 50 #7135 | Zbl 0269.14019

[12] A. Dold, Lectures on Algebraic Topology, Springer-Verlag, 1972. | MR 54 #3685 | Zbl 0234.55001

[13] T. Ekedahl et J.-P. Serre, Exemples de courbes algébriques à Jacobienne complètement décomposable, C.R. Acad. Sci. Paris 317, Série I (1993), 509-513. | MR 94j:14029 | Zbl 0789.14026

[14] B. H. Gross and J. Harris, Real algebraic curves, Ann. Scient. Éc. Norm. Sup. 14 (1981), 157-182. | Numdam | MR 83a:14028 | Zbl 0533.14011

[15] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math. 79 (1964), 109-326. | MR 33 #7333 | Zbl 0122.38603

[16] M. Hirsch, Differential Topology, New York and Berlin, Springer, 1976. | MR 56 #6669 | Zbl 0356.57001

[17] S. T. Hu, Homotopy Theory, New York, Academic Press, 1959. | MR 21 #5186 | Zbl 0088.38803

[18] S. Lang, Abelian Varieties, Interscience, New York, 1959. | MR 21 #4959 | Zbl 0098.13201

[19] H. Lange, Produkte elliptischer Kurven, Nachr. Akad. Wiss. Göttingen 8 (1975), 95-108. | MR 58 #22088 | Zbl 0317.14022

[20] H. Lange and Ch. Birkenhake, Complex Abelian Varieties, Grundlehren der Math. Wissenschaften, vol. 302, Springer-Verlag, 1992. | MR 94j:14001 | Zbl 0779.14012

[21] J.-L. Loday, Applications algébriques du tore dans la sphère et du Sp X Sq dans Sp + q, Algebraic K-Theory II, Lecture Notes in Math., vol. 342, 79-91, Springer-Verlag, 1973, p. 79-91. | MR 51 #4276 | Zbl 0269.57001

[22] J. S. Milne, Jacobian varieties, in Arithmetic Geometry, edited by G. Cornell and J. H. Silverman, Springer-Verlag, 1986, p. 167-212. | MR 861976 | Zbl 0604.14018

[23] Y. Namikawa, Toroidal Compactification of Siegel Spaces, Lecture Notes in Math. vol. 812, Springer-Verlag, 1980. | MR 82a:32034 | Zbl 0466.14011

[24] S. M. Natanzon, Moduli spaces of real curves, Trans. Moscow Math. Soc. Issue 1 (1980), 233-272. | Zbl 0452.14006

[25] M. Seppälä, Moduli space of stable real algebraic curves, Ann. Scient. Éc. Norm. Sup. 24 (1991), 519-544. | Numdam | MR 93b:14047 | Zbl 0757.32011

[26] M. Seppälä and R. Silhol, Moduli spaces for real algebraic curves and real abelian varieties, Math. Zeitschrift 201 (1989), 151-165. | MR 90k:14043 | Zbl 0645.14012

[27] J.-P. Serre, Faisceaux algébriques cohérents, Ann. of Math. 61 (1955), 197-278. | MR 16,953c | Zbl 0067.16201

[28] I. R. Shafarevich, Basic Algebraic Geometry, Springer-Verlag, 1977. | MR 56 #5538 | Zbl 0362.14001

[29] R. Silhol, Real Algebraic Surfaces, Lecture Notes in Math. vol. 1392, Springer-Verlag, 1989. | MR 91i:14045 | Zbl 0691.14010

[30] R. Silhol, Compactifications of moduli spaces in real algebraic geometry, Invent. Math. 107 (1992), 151-201. | MR 93i:14018 | Zbl 0777.14014

[31] R. G. Swan, Vector bundles and projective modules, Trans. Amer. Math. Soc. 105 (1962), 264-277. | MR 26 #785 | Zbl 0109.41601

[32] R. G. Swan, Topological examples of projective modules, Trans. Amer. Math. Soc. 230 (1977), 201-234. | MR 56 #6657 | Zbl 0443.13005