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Projective line

About: Projective line is a research topic. Over the lifetime, 2066 publications have been published within this topic receiving 31772 citations.


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Book
24 Jan 1980
TL;DR: The first properties of the plane can be found in this article, where the authors define the following properties: 1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. Ovals 9. Arithmetic of arcs of degree two 10. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes 15.
Abstract: 1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. First properties of the plane 8. Ovals 9. Arithmetic of arcs of degree two 10. Arcs in ovals 11. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes Appendix Notation References

1,593 citations

Journal ArticleDOI
TL;DR: In this article, a universal system of differential equations is proposed to determine the generating function of the Chern classes of the Hodge bundle in Gromov-Witten theory for any target X. The genus g, degree d multiple cover contribution of a rational curve is found to be simply proportional to the Euler characteristic of M_g.
Abstract: Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these integrals from the standard descendent potential (for any target X). We use virtual localization and classical degeneracy calculations to find trigonometric closed form solutions for special Hodge integrals over the moduli space of pointed curves. These formulas are applied to two computations in Gromov-Witten theory for Calabi-Yau 3-folds. The genus g, degree d multiple cover contribution of a rational curve is found to be simply proportional to the Euler characteristic of M_g. The genus g, degree 0 Gromov-Witten invariant is calculated (in agreement with recent string theoretic calculations of Gopakumar-Vafa and Marino-Moore). Finally, with Zagier's help, our Hodge integral formulas imply a general genus prediction of the punctual Virasoro constraints applied to the projective line.

603 citations

Book
01 Jan 1988
TL;DR: In this paper, the authors present a collection of papers dedicated to L. Cayley's work on algebraic surfaces, including the following: A. COBLE, Algebraic geometry and theta functions, A. CAYLEY, A memoir on quartic surfaces.
Abstract: [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. | MR 374411 | Zbl 0313.32029 [ACGH] E. ARBARELLO, M. CORNALBA, P. GRIFFITHS, J. HARRIS, Geometry of algebraic curves, vol. I, Springer -Verlag. 1984. | Zbl 0559.14017 [AS] Algebraic surfaces (ed. by I.Shafarevich), Proc.SteKlov.Math.Inst., v. 75. 1964. [Engl.transl: AMS, Providence . R.I. 1967]. | MR 190143 [Ba] H. BAKER, Principles of geometry, vol. IV. Frederick Unger Publ. New York. 1925 (republished by Cambridge Univ.Press. 1963). | MR 178393 [Be] A. BEAUVILLE, Variétés de Prym et jacobiennes intermédiaires, Ann. Sci. Ecole Norm. Sup. 10 (1977), 309-331. | Article | Numdam | MR 472843 | Zbl 0368.14018 [Bo] N. BOURBAKI, Groupes et algèbres de Lie. Chapters IV-VI. Herman. Paris. 1966 [Russ. transl.: Mir. Moscow. 1972]. | Zbl 0483.22001 [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). | MR 847340 | Zbl 0615.14031 [Br ] G. BREDON. Introduction to compact transformation groups. Academic Press. 1972 [Russ. Transl.: Nauka. Moscow. 1980]. | MR 617738 | Zbl 0484.57001 [Ca] A. CAYLEY, A memoir on quartic surfaces . Proc. London Math.Soc, 3 (1869/71), 19-69, | JFM 03.0390.01 | MR 1577187 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 55.0808.02 | MR 733252 [Co 2] A. COBLE, Point sets and allied Cremona groups, I , Trans. Amer. Math. Soc. 16 (1915), 155-198. | JFM 45.0234.01 | MR 1501008 [Co 3] A. COBLE, Point sets and allied Cremona groups, II , Trans. Amer. Math. Soc. 17 (1916), 345-388. | JFM 45.0234.01 | MR 1501047 [Co 4] A. COBLE, Point sets and allied Cremona groups. III , Trans. Amer. Math. Soc. 18 (1917), 331-372. | JFM 46.0890.01 | MR 1501073 [Co 5] A. COBLE, Associated sets of points. Trans. Amer.Math.Soc. 24 (1922), 1-20. | Article | JFM 49.0490.01 | MR 1501210 [Co 6] A. COBLE, The ten nodes of the rational sextic and of the Cayley symmetroid . Amer. J. Math. 41 (1919), 243-265. | Article | JFM 47.0596.01 | MR 1506391 [Co 7] A. COBLE, Theta modular groups determined by point sets. Amer. J. Math., 40 (1918), 317-340. | Article | JFM 46.0612.04 | MR 1507902 [Co 8] A. COBLE, Configurations defined by theta functions, Duke Math. J., 5 (1939), 479-488. | Article | MR 160 | Zbl 0022.16304 [Coo] J. COOLIDGE, A treatise on algebraic plane curves. Dover Publ. 1959. | MR 120551 | Zbl 0085.36403 Bibliographie Rechercher des articles, des livres... Tout + 

375 citations

Journal ArticleDOI
TL;DR: In this paper, the authors construct moduli spaces for weighted pointed curves using methods of the log minimal model program, and describe the induced birational morphisms between moduli space as the weights are varied.

366 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202323
202235
202185
202070
201970
201881