Point sets in projective spaces and theta functions
Astérisque, no. 165 (1988) , 222 p.
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     title = {Point sets in projective spaces and theta functions},
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     number = {165},
     year = {1988},
     zbl = {0685.14029},
     mrnumber = {1007155},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1988__165__1_0/}
}
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Dolgachev, Igor; Ortland, David. Point sets in projective spaces and theta functions. Astérisque, no. 165 (1988), 222 p. http://numdam.org/item/AST_1988__165__1_0/

[Ac] R. Accola, Some loci of Teichmüller space for genus five defined by vanishing theta nulls, in "Contribution to analysis" (a collection of papers dedicated to L. Bers), Academic Press, New York. 1974, pp. 11-18. | Zbl | MR

[ACGH] E. Arbarello, M. Cornalba, P. Griffiths, J. Harris, Geometry of algebraic curves, vol. I, Springer -Verlag. 1984. | Zbl

[AS] Algebraic surfaces (ed. by I.Shafarevich), Proc.SteKlov.Math.Inst., v. 75. 1964. [Engl.transl: AMS, Providence . R.I. 1967]. | MR

[Ba] H. Baker, Principles of geometry, vol. IV. Frederick Unger Publ. New York. 1925 (republished by Cambridge Univ.Press. 1963). | MR

[Be] A. Beauville, Variétés de Prym et jacobiennes intermédiaires, Ann. Sci. Ecole Norm. Sup. 10 (1977), 309-331. | DOI | Numdam | EuDML | Zbl | MR

[Bo] N. Bourbaki, Groupes et algèbres de Lie. Chapters IV-VI. Herman. Paris. 1966 [Russ. transl.: Mir. Moscow. 1972]. | Zbl

[Bog] F. Bogomolov, Stable rationality of factor spaces for simply connected groups, Mat. Sbornik 130 (1986), 3-17 [Engl. Transl.: Mathematics of USSR-Sbornik, 58 (1987), 1-17). | Zbl | MR

[Br ] G. Bredon. Introduction to compact transformation groups. Academic Press. 1972 [Russ. Transl.: Nauka. Moscow. 1980]. | MR | Zbl

[Ca] A. Cayley, A memoir on quartic surfaces. Proc. London Math.Soc, 3 (1869/71), 19-69, | MR | JFM

A. Cayley, A memoir on quartic surfacesCol. works, VII, Cambridge Univ. Press. 1894, 133-181.

[Co 1] A. Coble, Algebraic geometry and theta functions, Amer. Math. Soc. Coll. Publ. 10, Providence, R.I., 1929 (3d ed., 1969). | JFM | MR

[Co 2] A. Coble, Point sets and allied Cremona groups, I, Trans. Amer. Math. Soc. 16 (1915), 155-198. | JFM | MR

[Co 3] A. Coble, Point sets and allied Cremona groups, II, Trans. Amer. Math. Soc. 17 (1916), 345-388. | JFM | MR

[Co 4] A. Coble, Point sets and allied Cremona groups. III, Trans. Amer. Math. Soc. 18 (1917), 331-372. | JFM | MR

[Co 5] A. Coble, Associated sets of points. Trans. Amer.Math.Soc. 24 (1922), 1-20. | DOI | JFM | MR

[Co 6] A. Coble, The ten nodes of the rational sextic and of the Cayley symmetroid. Amer. J. Math. 41 (1919), 243-265. | DOI | JFM | MR

[Co 7] A. Coble, Theta modular groups determined by point sets. Amer. J. Math., 40 (1918), 317-340. | DOI | JFM | MR

[Co 8] A. Coble, Configurations defined by theta functions, Duke Math. J., 5 (1939), 479-488. | DOI | Zbl | MR

[Coo] J. Coolidge, A treatise on algebraic plane curves. Dover Publ. 1959. | Zbl | MR

[Cos] F. Cossec, Reye congruences. Trans. Amer. Math. Soc. 280 (1983), 737-751. | DOI | Zbl | MR

[C-D 1] F. Cossec, I. Dolgachev, On automorphisms of nodal Enriques surfaces. Bull. Amer. Math. Soc. 12 (1985), 247-249. | DOI | Zbl | MR

[C-D 2] F. Cossec, I. Dolgachev, Enriques surfaces I, Birkäuser Boston, 1988. | Zbl | MR

[C-D 3] F. Cossec, I. Dolgachev, Enriques surfaces II (in preparation).

[Da] V. Danilov, On decomposition of certain birational morphisms, Izv. Akad. Nauk SSSR, Ser. Math. 44 (1980), 465-477 [Engl. transl.: Mathematics of USSR-lzvestija, 16 (1981), 419-4291. | Zbl | MR

[De] M. Demazure, Surfaces de del Pezzo, II-V, Lect.Notes in Math. v. 777, 1980, 23-69. | Numdam | Zbl

[De-P] C. De Concini, C. Procesi, A characteristic free approach to invariant theory, Adv. Math. 21 (1976), 330-354. | DOI | Zbl | MR

[Di-C] J. Dieudonné, J. Carrel, Invariant theory, old and new. Acad. Press, 1971. [Russ. transl.: Mir. Moscow. 1974]. | Zbl | MR

[Do 1] I. Dolgachev, Weyl groups and Cremona transformations. Proc. Symp. Pure Math. 40 (1983), 283-294. | DOI | Zbl | MR

[Do 2] I. Dolgachev, Automorphisms of Enriques surfaces. Invent. Math. 76 (1984), 63-177. | DOI | EuDML | Zbl | MR

[DuV 1] P. Du Val, On isolated singularities which do not affect the condition of adjunction, I, II, IV, Proc. Cambridge Phil. Soc. 30 (1934), 453-491. | DOI | JFM

[DuV 2] P. Du Val, On the Kantor group of a set of points in a plane, Proc. London Math. Soc. 2) 42 (1936), 18-51. | JFM | MR

[DuV 3] P. Du Val, Application des idées crystallographiques à l'étude des groupes de transformations crémoniennes, Colloq. de Géom. Algébrique. Bruxelles. 1959. | Zbl

[DuV 4] P. Du Val, Crystallography and Cremona transformations., 191-201. in "The geometric vein", Springer-Verlag, 1981, pp. 191-201. | DOI | Zbl | MR

[Fay] J. Fay, Theta functions on Riemann surfaces, Lect. Notes in Math. vol. 352, Springer-Verlag. 1973. | Zbl | MR

[Fr 1] G. Frobenius, Über die Beziehungen zwischen den 28 Doppeltangenten einer ebenen Curve vierter Ordnung, Journ.für die reine und angew. Mathematik, 99 (1886), 275-314 (Gesammelte Abhandlungen, Band II, Springer-Verlag. 968, pp. 262-300). | EuDML | JFM | MR

[Fr 2] G. Frobenius, Uber die Jacobischen Functionen dreier Variabein, Journ. für die reine und angew. Mathematik, 105 (1889), 35-100 | EuDML | JFM | MR

G. Frobenius, Uber die Jacobischen Functionen dreier Variabein (Gesammelte Abhandlungen, B. II, Springer-Verlag. 1968, pp. 383- 448). | MR

[Fo] J. Fogarty, Algebraic families on an algebraic surface. II, Amer. J. Math, 95 (1973), 660-687. | DOI | Zbl

[vG 1] B. Van Geemen, The moduli space of curves of genus 3 with level 2 structure is rational (preprint).

[vG 2] B. Van Geemen, Schottky-Jung relations and vector bundles on hyperelliptic curves (preprint). | Zbl | MR

[vG 3] B. Van Geemen, Siegel modular forms vanishing on the moduli space of curves, Invent. Math. 78 (1984), 329-349. | DOI | EuDML | Zbl | MR

[vG-vdG] B. Van Geemen, G. Van Der Geer, Kummer varieties and the moduli spaces of abelian varieties, Amer. J. Math. 108 (1986), 615-642. | DOI | Zbl | MR

[vdG] G. Van Der Geer, On the geometry of a Siegel modular 3-fold, Math. Ann., 260 (1982), 17-350. | DOI | EuDML | Zbl | MR

[Gi] M. Gizatullin, Rational G-surfaces, Izv.AKad. NauK SSSR, Ser. Math. 44 (1980) [Engl. transl.: Mathematics of USSR Izvestija, 16 (1981), 103-134]. | Zbl | MR

[Gr] D. Grant, A generalization of Jacobi derivative formula to dimension two (preprint). | Zbl

[Gri 1] R. Griess, Quotients of infinite reflection groups. Math. Ann., 263 (1983), 267-288. | DOI | EuDML | Zbl | MR

[Gri 2] R. Griess, The Monster and its nonassociative algebra, Contemp. Math., V. 45 (1985), 121-157. | DOI | Zbl | MR

[Gr-H] P. Griffiths, J. Harris, Principles of algebraic geometry. Wiley, New York. 1978 [Russ. transl.: Mir. Moscow. 1982]. | Zbl | MR

[Ha 1] B. Harbourne, Iterated blow-ups and moduli for rational surfaces. (preprint). | DOI | Zbl | MR

[Ha 2] B. Harbourne, Blowings-up of P 2 and their blowings-down, Duke math. J. 52 (1985), 129-148. | DOI | Zbl | MR

[Ha1] M. Halphen, Sur les courbes planes du sixième degré a neuf points doubles, Bull. Soc. Math. France, 10 (1981), 162-172. | Numdam | EuDML | JFM | MR

[Hi] A. Hirschowitz, Symétrie des surfaces rationnelles génériques, Math. Ann. 281 (1988), 255-262. | DOI | EuDML | Zbl | MR

[Hu] R. Hudson, Kummer's quartic surface. Cambridge Univ. Press. 1905. | JFM | MR

[Ig 1] J. Igusa, Theta functions. Springer Verlag. 1972. | Zbl | MR

[Ig 2] J. Igusa, A desingularization problem in the theory of Siegel modular functions. Math. Ann., 168 (1967), 228-260. | DOI | EuDML | Zbl | MR

[|g3] J. Igusa, On Siegel modular forms of genus 2 (II), Amer. J. Math. 86 (1964), 392-412. | DOI | Zbl | MR

[Ish] S. Ishii, Moduli space of polarized Del Pezzo surfaces and its compactification, Tokyo Math. J., 5 (1982), 289-297. | DOI | Zbl | MR

[Jes] C. Jessop, A treatise on the line complex. Cambridge. 1903 (new edition: Chelsea Publ. New York. 1969). | Zbl | MR

[Ka] S. Kantor, Theorie der endlichen Gruppen von eigendeutigen Transformationen in der Ebenen. Berlin. 1895. | JFM

[Kac] V. Kac, Infinite-dimensional Lie algebras. Birkhäuser. Boston. 1983. | Zbl | MR

[Kal] A. Kalker, Cubic fourfolds with fifteen ordinary double points, Dissertation at Univ. Leiden, 1986.

[Ki 1] F. Kirwan, Cohomology of quotients in symplectic and algebraic geometry. Math. Notes 31, Princeton Univ. Press. 1984. | Zbl | MR

[Ki 2] F. Kirwan, Partial desingularization of quotients of non-singular varieties and their Betti numbers, Ann. Math. 122 (1985), 41-85. | DOI | Zbl | MR

[Kl] S. Kleiman, Multiple-point formulas I, Acta Math. 147 (1981), 13-49. | DOI | Zbl | MR

[Ko] M. Koitabashi, Automorphism groups of generic rational surfaces, J. Algebra, 116 (1988), 130-142. | DOI | Zbl | MR

[Lo 1] E. Looijenga, Rational surfaces with an anticanonical cycle, Ann. Math. (2) 114 (1981), 267-322. | DOI | Zbl | MR

[Lo 2] E. Looijenga, Invariant theory for generalized root systems. Invent. Math. 61 (1980), 1-32. | DOI | EuDML | Zbl | MR

[Ma] Y. Manin, Cubic forms. Nauka. Moscow. 1972 [Engl, transl.: North-Holland, Amsterdam. 1974, 2nd edition 1986]. | MR | Zbl

[Mat] A. Mattuck, Arthur Byron Coble, Bull.A.M.S., 76 (1970), 693-699. | DOI | Zbl | MR

[Med 1] I. Macdonald, Symmetric functions and Hall polynomials. Clarendon Press. Oxford. 1979 [Russ. transl.: Mir. Moscow. 1985]. | Zbl | MR

[Med 2] I. Macdonald, Some irreducible representations of Weyl groups. Bull. London Math. Soc., 4 (1972), 148-150. | DOI | Zbl | MR

[Mo] E. Moore, The cross-ratio group of n! Cremona transformations of order n-3 in flat space of n-3 dimensions, Amer.J.Math., 22 (1900), 336-342. | DOI | MR | JFM

[Mu 1] D. Mumford, Geometric invariant theory. Springer. 1965 (new ed. with J. Fogarty, Springer 1986). | Zbl | MR

[Mu 2] D. Mumford, Lectures on theta II. Progr. in Math., 43, Birkhäuser. 1984. | Zbl | MR

[Mu 3] D. Mumford, Abelian varieties. Oxford University Press. 1969 [Russ. trans.: Mir. Moscow. 1971]. | Zbl | MR

[Mu 4] D. Mumford, Theta characteristics of an algebraic curve, Ann. Sci. Ecole Norm.Sup. 4 (1971), 181-192 | DOI | Numdam | EuDML | Zbl | MR

[Mu 5] D. Mumford, On equations defining abelian varieties, I, Invent. Math. 1 1966), 287-354 [Russ. transl.: Matematika, 14:1 (1970), 104-136]. | DOI | Zbl | EuDML | MR

[Na] M. Nagata, On rational surfaces, II, Mem. Coll. Sci. Univ. Kyoto, 33 (1960), 271-293. Russ. Transl.: Matematika, 8:4 (1964), 75-941. | DOI | Zbl | MR

[N-R] M. Narasimhan, S. Ramanan, 2 θ -linear systems on abelian varieties, in "Vector bundles on algebraic varieties", Oxford Univ. Press. 1987. | Zbl | MR

[Or] D. Ortland, Moduli of finite point sets in projective space, Ph.D. thesis, Univ. of Michigan, 1984. | MR

[Pi] H. Pinkham, Résolution simultanée de points doubles rationnels. Lect. Notes in Math. v. 777, Springer-Verlag, 1980, 179-204. | DOI | Numdam | Zbl

[Ra] Z. Ran, Enumerative curvilinear geometry, Acta Math, 155 (1985), 81-90. | DOI | MR | Zbl

[Re] L. Renner, Binary quintics, in Conference Proc. of Canadian Math. Soc, 6 (1986), 369-376. | Zbl | MR

[Rei] Z. Reichstein, The behavior of stability under equivariant maps. Thesis. MIT. 1988. | MR

[Sa] R. Sasaki, Modular forms vanishing at the reducible points of the Siegel upper half-space, J. fur die reine und angew. Mathematik, 345 (1983), 111-123. | EuDML | Zbl | MR

[S-R] J. Semple, L. Roth, Introduction to algebraic geometry. Clarendon Press, Oxford. 1949. | Zbl | MR

[SB] N. Shepherd-Barron, The Siegel modular threefold of level three (preprint).

[Sen 1] F. Schottky, Eine algebraische Untersuchung über Thetafunktionen von drei Argumenten, Journ. für Math. 105 (1889), 268-297. | EuDML | JFM | MR

[Sch 2] F. Schottky, Über die Moduln der Thetafunctionen, Acta Math. 27 (1903), 235-288. | DOI | JFM | MR

[Sch 3] F. Schottky, Abriss einer Theorie der Abelschen Functionen von drei Variabein. Teubner. Leipzig. 1880. | JFM

[Sh] V. Shokurov, The Noether-Enriques theorem on canonical curves. Mat. Sbornik 86 (1971), 361-403 [English transl.: Mathematics of USSR-Sbornik, 15 (1971), 361-403). | DOI | Zbl

[Sz] M. Szurek, Binary quintics with involutions, in Conference Proc. of Canadian Math. Soc., 6 (1986), 473-476. | Zbl

[Ta] Y.-S. Tai, On the Kodaira dimension of the moduli space of abelian varieties, Invent. Math. 68 (1982), 425-439. | DOI | EuDML | Zbl | MR

[Th] R. Thomae, Beitrag zur Bestimmungen von θ(0) der die Klassenmoduln algebraischer Functionen, J. für die reine und angew. Math., 71 (1870), 201-222. | DOI | JFM | MR | EuDML

[Ti] G. Timms, The nodal cubic surfaces and the surfaces from which are derived by projections, Proc. Roy. Soc, Ser. A, 119 (1928), 213-248. | DOI | JFM

[Ty 1] A. Tyurin, On intersection of quadrics, Uspehi Mat. Nauk, 30, No 6 (1975), 51-99 [Engl.Transl: Russ. Math. Surveys, 30, No 6, 51-1051. | Zbl | MR

[Ty 2] A. Tyurin, Special zero-cycles on polarized K3 surfaces, Izv. Akad. NauK SSSR, Ser. Math, 51, No 1 (1987). | Zbl

[Ur] T. Urabe, On singularities on degenerate Del Pezzo surfaces of degree 1,2, in Proc. Symp. Pure Math., v. 40. Part I, 1983, pp. 587-591. | DOI | Zbl | MR

[Vi] E. Vinberg, Discrete groups generated by reflections, lzv, Akad. NauK SSSR, Ser. Math. 51 (1971) [Engl. Transl.: Math. USSR-Izvestija, 5 (1971), 1083-1119]. | Zbl

[Wi 1] W. Wirtinger, Untersuchungen über Thetafunctionen. Teubner, Leipzig. 1895. | JFM

[Wi 2] W. Wirtinger, Untersuchungen über Abel'schen Functionen vom Geschlechte drei. Math. Ann., 1940 (1892), 261-312. | DOI | EuDML | JFM | MR