[For elliptic curves see number theory.] -------------------------------------------------- 5126 Shreeram Abhyankar: What is the difference between a parabola and a hyperbola. Math. Intell. 10/4 (1988), 36-43. 1513 William Abikoff: The real analytic theory of Teichmueller space. SLN Math. 820 (1980). 4865 William Abikoff: Moduli of Riemann surfaces. 4859 Bers/Kra, 79-93. R. Accola: Topics in the theory of Riemann surfaces. SLN Math. 1595 (1994), 110p. 3-540-58721-7. DM 34. Lars Ahlfors/Lipman Bers/Hershel Farkas/Robert Gunning/Irwin Kra/Harry Rauch (e.d.): Advances in the theory of Riemann surfaces. Princeton UP 1971. 24323 Samuele Anni: Alcuni risultati sulla teoria delle superficie di Riemann. Tesi LT Univ. Pavia 2007, 66p. 2791 Enrico Arbarello/Maurizio Cornalba/Phillip Griffiths/J. Harris: Geometry of algebraic curves. 2 volumes. Springer 1985. W. Baily: On moduli of Jacobian varieties. Annals Math. 71 (1960), 303-314. H. Baker: Abelian functions, Abel's theorem and the allied theory of theta functions. Cambridge UP 1995, 690p. 0-521-49877-5. Pds. 28. Edoardo Ballico: Real moduli of complex objects: Surfaces and bundles. Monatshefte Math. 115 (1993), 13-26. 20599 Arnaud Beauville: Prym varieties and the Schottky problem. Inv. Math. 41 (1977), 149-196. 20600 Arnaud Beauville: L'approche geometrique du probleme de Schottky. Proc. ICM Berkeley 1987, 6p. 20602 Arnaud Beauville: Vector bundles on curves and theta functions. Adv. Studies Pure Math. 45 (2006), 145-156. 23952 E. Belokolos/Alexander Bobenko/V. Enolskii/A. Its/V. Matveev: Algebro-geometric approach to nonlinear integrable equations. Springer 1994, 350p. 27150 Alessandra Bernardi/Alessandro Gimigliano/Monica Ida': Singularities of plane rational curves via projections. Arxiv 1609.01877 (2016), 23p. R. Bix: Conics and cubics. Springer 2006, 350p. Eur 25. 23980 Janko Böhm: Parametrisierung rationaler Kurven. Diplomarbeit Univ. Bayreuth ca. 2000, 200p. R. Bix: Conics and cubics. Springer 1998, 290p. DM 98. An elementary concrete (and expensive) introduction. " ... der Autor trotzdem bis zum Beweis des Satzes von Bezout kommt ... Aber es wird demonstriert ... wie weit man mit elementarster analytischer Geometrie in die Theorie der ebenen algebraischen Kurven vordringen kann." (H. Stachel) 23960 Alexander Bobenko: Introduction to compact Riemann surfaces. Internet ca. 2007, 61p. 4803 Jean-Benoit Bost: Introduction to compact Riemann surfaces, Jacobians, and Abelian varieties. 4740 Waldschmidt, 64-211. P. Buser: Geometry and spectra of compact Riemann surfaces. Birkhaeuser 1992, 450p. 3-7643-3406-1. SFR 124. "Mit diesem Buch wird ein Werk von hoher Qualitaet vorgelegt, das einerseits die geometrische Theorie kompakter Riemannscher Flaechen vom Geschlecht > 1 behandelt und andererseits die Beziehungen des Laplaceoperators mit der Geometrie kompakter Riemannscher Flaechen zum Thema hat. Diese beiden Fragenkomplexe werden in diesem Buch ausfuehrlich und sorgfaeltigst behandelt. [...] Das Buch kann gar nicht hoch genug gelobt werden. Ein schwieriges und interessantes Gebiet der Analysis wird darin in beeindruckender Form dargestellt." (F. Schnitzer) 24324 Maurizio Cailotto: Superfice di Riemann compatte. Internet 2006, 65p. Lucia Caporaso/Joe Harris: Counting plane curves of any genus. Inv. Math. 131/2 (1998), 345-392. 20821 James Carlson/Philipp Griffiths: What is a period domain? Notices AMS December 2008, 1418-1419. E. Casas-Alvero: Singularities of plane curves. Cambridge UP 2000, 350p. $48. Renzo Cavalieri/Eric Miles: Riemann surfaces and algebraic curves. CUP 2016, 190p. Eur 35. Shiing-shen Chern: An elementary proof of the existence of isothermal parameters on a surface. Proc. AMS 6 (1955), 771-782. 3337 Claude Chevalley: Introduction to the theory of algebraic functions of one variable. AMS 1951. 21832 Ludovica Chiodera: Sistemi lineari, singolarita' delle curve piane e superfici razionali. Tesi LS Ferrara 2008, 80p. Ciro Ciliberto: Alcuni aspetti della classificazione delle famiglie di curve in uno spazio proiettivo. Boll. UMI 10-A (1996), 491-535. C. Clemens: A scrapbook of complex curve theory. AMS 2003, 190p. $39. 2071 Harvey Cohn: Conformal mapping on Riemann surfaces. Dover 1967. 22302 Alberto Collino: A simple proof of the theorem of Torelli based on Torelli's approach. Proc. AMS 100/1 (1987), 16-20. J. Coolidge: A treatise on algebraic plane curves. Dover 1959. Pierre Deligne/David Mumford: Irreducibility of the space of curves of a given genus. Publ. IHES 36 (1969), 75-109. 22685 Olivier Dodane: Theoremes de Petri pour les courbes stables et degenerescence du systeme d'equations du plongement canonique. Internet 2009, 90p. 27551 Simon Donaldson: Riemann surfaces. Oxford UP 2011, 290p. Eur 36. 3368 K. Doi/H. Naganuma: On the algebraic curves uniformized by arithmetical automorphic functions. Annals Math. 86 (1967), 449-460. 22420 David Eisenbud/Joe Harris: Progress in the theory of complex algebraic curves. Bull. AMS 21/2 (1989), 205-232. 23964 Matthew England/Chris Athorne: Building abelian functions with generalised Baker-Hirota operators. SIGMA 8 (2012), 36p. Gerd Faltings: Stable G-bundles and projective connections. J. Alg. Geom. 2 (1993), 507-568. 20091 Gerd Faltings: Thetafunktionen auf Modulräumen von Vektorbündeln. Jber. DMV 110/1 (2008), 3-17. 22594 Gavril Farkas: The birational geometry of the moduli space of curves. Diss. Univ. Amsterdam 2000, 98p. 22448 Gavril Farkas: The geometry of the moduli space of curves of genus 23. Math. Ann. 318 (2000), 43-65. 22593 Gavril Farkas: Syzygies of curves and the effective cone of M_g. Duke Math. J. 135 (2006), 53-98. 22459 Gavril Farkas: Rational maps between moduli spaces of curves and Gieseker-Petri divisors. J. Alg. Geom. 19 (2010), 243-284. 22445 Gavril Farkas: Prym varieties and their moduli. Internet 2011, 35p. 22462 Gavril Farkas/Alessandro Verra: The intermediate type of certain moduli spaces of curves. Internet ca. 2010, 18p. 3611 Hershel Farkas/Irwin Kra: Riemann surfaces. Springer 1992, 360p. Maria Rita Ferraro: Curve trigonali immergibili come intersezioni complete insiemistiche. Tesi, Ferrara 1993. 18346 Gerd Fischer: Ebene algebraische Kurven. Vieweg 1994, 170p. Eur 26. 2007 Kuno Fladt: Analytische Geometrie spezieller ebener Kurven. Akad. Verlagsgesellschaft 1962. E. Flynn: The group law on the Jacobian of a curve of genus 2. J. reine u. angew. Math. 439 (1993), 45-69. 1465 Otto Forster: Riemannsche Flaechen. Springer 1977. 21633 Eberhard Freitag: Funktionentheorie 2. Springer 2009, 520p. Eur 39. William Fulton: Algebraic curves. Addison-Wesley 1989. 5206 Gerard van der Geer: The Schottky problem. SLN Math. 1111 (1985), 385-406. 2813 Franco Ghione/C. Peskine/Edoardo Sernesi (ed.): Space curves. SLN Math. 1266 (1987). Christopher Gibson: Elementary theory of algebraic curves. Cambridge UP 2008, 270p. Eur 35. 2810 D. Gieseker: Lectures on moduli of curves. Springer 1982. 4923 Leon Greenberg (ed.): Discontinuous groups and Riemann surfaces. Princeton UP 1974. 3548 Phillip Griffiths: Introduction to algebraic curves. AMS 1989. [AMS 1995, 500p. 0-8218-4537-3 (pb). Pds. 30.] Phillip Griffiths: Variations on a theorem of Abel. Inv. Math. 35 (1976), 321-390. 18038 Phillip Griffiths/Joseph Harris: Principles of algebraic geometry. Wiley 1994, 810p. Eur 94. [or 1471 Phillip Griffiths/Joseph Harris: Principles of algebraic geometry. Wiley 1978.] J. Guenot/R. Narasimhan: Introduction a' la theorie des surfaces de Riemann. L'Ens. Math. 21 (1975), 123-328. 1515 Robert Gunning: Vorlesungen ueber Riemannsche Flaechen. Bibl. Inst. 1972. 20542 Günter Harder: Lectures on algebraic geometry 1. Sheaves, cohomology of sheaves, and applications to Riemann surfaces. Vieweg 2008, 290p. Eur 54. A very readable and thorough introduction to geometric homological algebra. 22421 Joe Harris/Ian Morrison: Moduli of curves. Springer 1998, 380p. 22665 Herwig Hauser/Georg Regensburger: Explizite Auflösung von ebenen Kurvensingularitäten in beliebiger Charakteristik. Ens. Math. 50 (2004), 305-353. 2812 Wilhelm Hauser/Werner Burau: Integrale algebraischer Funktionen und ebene algebraische Kurven. Berlin 1958. 3476 Kurt Hensel/Georg Landsberg: Theorie der algebraischen Funktionen einer Variablen. Chelsea 1965. 22423 Maarten Hoeve: An introduction to moduli spaces of curves. Internet 2007, 9p. A. Howard/A. Sommese: On the theorem of De Franchis. Ann. SNS Pisa 10 (1983), 429-436. J. Jost: Compact Riemann surfaces. Springer 2002, 280p. Eur 40. 29166 Ott-Heinrich Keller: Cremona-Transformationen algebraischer Kurven. Crelle 169/4 (1933), 193-218. Ott-Heinrich Keller: Die Weierstrasskurven einer algebraischen Kurve. Jber. DMV 45 (1935), 74-75. 5194 Ott-Heinrich Keller: Berechnung eines Primideals aus seiner allgemeinen Nullstelle. Math. Zeit. 87 (1965), 160-162. Keller entwickelt hier einen Algorithmus zur Berechnung der definierenden Gleichungen der rationalen Raumkurve 4. Ordnung. Ein nichttriviales Beispiel. 5376 George Kempf: On the geometry of a theorem of Riemann. Annals Math. 98 (1973), 178-185. 5377 George Kempf: Inversion of abelian integrals. Bull. AMS 6 (1982), 25-32. 22454 Frances Kirwan: Complex algebraic curves. Cambridge UP 1995, 260p. Eur 41. 22783 Stephan Klaus/Oliver Labs/Thomas Markwig: Theorie und Visualisierung algebraischer Kurven und Flächen. Internet 2009, 130p. 26907 Werner Kleinert: Review of the book "Algebraic curves and Riemann surfaces" by Rick Miranda. ZB 0820.14022, 4p. 27099 G. Kohn: Spezielle ebene algebraische Kurven. Internet, 115p. 22768 Irwin Kra: Review of the book "Riemann surfaces" by Simon Donaldson. Bull. AMS ... (2012), 9p. 4922 H. Kuenzi/A. Pfluger (ed.): Festband zum 70. Geburtstag von Rolf Nevanlinna. Springer 1966. 22291 Ernst Kunz: Introduction to plan algebraic curves. Birkhäuser 2005, 290p. Eur 58. 17903 Klaus Lamotke: Riemannsche Flächen. Springer 2005, 320p. Eur 39. 3593 Serge Lang: Introduction to algebraic and abelian functions. Springer 1982. 2290 Dennis Lawrence: A catalog of special plane curves. Dover 1972. 457 Jacobus van Lint/Gerard van der Geer: Introduction to coding theory and algebraic geometry. Birkhaeuser 1988. Qing Liu: Algebraic geometry and arithmetic curves. Oxford UP 2002, 460p. Pds 40. 27100 Gino Loria: Spezielle ebene algebraische Kurven von höherer als der vierten Ordnung. Internet, 65p. Yuri Manin: Quantum strings and algebraic curves. Berkeley ICM talk 1986. 3578 Mireille Martin-Deschamps/Daniel Perrin: Sur la classification des courbes gauches. Asterisque 184-185 (1990). Mireille Martin-Deschamps/Daniel Perrin: Courbes gauches et modules de Rao. J. reine u. angew. Math. 439 (1993), 103-145. 4935 Barry Mazur: Arithmetic on curves. Bull. AMS 14 (1986), 207-259. 20512 Jörg Meyer: Die räumliche Parabel mit dem allgemeinen Punkt (t,t^2,t^3). Teach. Math. 6/1 (2003), 49-66. 5051 Rick Miranda: Algebraic curves and Riemann surfaces. AMS 1995, 400p. 22237 Rick Miranda: Linear systems of plane curves. Notices AMS 46/2 (1999), 192-202. 2816 M. Miyanishi: Curves on rational and unirational surfaces. Springer 1978. Carlos Moreno: Algebraic curves over finite fields. Cambridge UP 1990, 270p. 0-521-34252-x. Pds. 30. Should be somewhat difficult to read. David Mumford: Curves and their jacobians. Univ. Michigan Press 1975. 1464 Makoto Namba: Geometry of projective algebraic curves. Dekker 1984. R. Narasimhan: Compact Riemann surfaces. Birkhaeuser 1992, 130p. 3-7643-2742-1. SFR 32. 2037 Rolf Nevanlinna: Uniformisierung. Springer 1967. Harald Niederreiter/Chaoping Xing: Rational points on curves over finite fields. Cambridge UP 2001, 250p. Pds. 40. A. Parshin/I. Shafarevich (ed.): Algebraic geometry III. Complex algebraic varieties - algebraic curves and their Jacobians. Springer 1997, 270p. DM 158. 4087 Eric Reyssat: Galois theory for coverings and Riemann surfaces. 4740 Waldschmidt, 394-412. 2072 Eric Reyssat: Quelques aspects des surfaces de Riemann. Birkhaeuser 1989. 25649 Andrea Scarpante: Il teorema di Ferrand-Szpiro. Tesi LT Univ. Ferrara 2014, 74p. Martin Schlichenmaier: Differential operator algebras on compact Riemann surfaces. 11 pages, 1993. ftp publications.math.duke.edu (get hep/9311036). 22273 Martin Schlichenmaier: An introduction to Riemann surfaces, algebraic curves and moduli spaces. Springer 2010, 220p. Eur 63. 8402 Klaus-Dieter Semmler/Mika Seppaelae: Numerical uniformization of hyperelliptic curves. Internet 1996 (Proc. ISSAC 95), 8p. 22231 J. Rafael Sendra/Franz Winkler/Sonia Perez-Diaz: Rational algebraic curves. Springer 2010, 270p. Eur 63. 8404 Mika Seppaelae: Computational conformal geometry. Internet 1994 (Invited main lecture at MEGA 94 in Santander), 7p. 8406 Mika Seppaelae/Robert Silhol: Riemann surfaces, plane algebraic curves and their period matrices. Internet, ca. 1993, 16p. Mika Seppaelae/Tuomas Sorvali: Geometry of Riemann surfaces and Teichmueller spaces. North-Holland 1992, 270p. $98. 20169 Edoardo Sernesi: A brief introduction to algebraic curves. Internet 1984, 25p. G. Springer: Introduction to Riemann surfaces. Addison-Wesley 1957. 22076 Henning Stichtenoth: Algebraic function fields and codes. Springer 2009, 350p. Eur 42. 2042 Oswald Teichmueller: Gesammelte Abhandlungen. Springer 1982. Ruggiero Torelli: Sulle varieta' di Jacobi. Rend. R. Acc. Lincei 22 (1913), 98-103. 24325 Cristina Turrini: Geometria complessa - superficie di Riemann I. Internet 2011, 64p. Dror Varolin: Riemann surfaces by way of complex analytic geometry. AMS 2011, 240p. Eur 65. William Veech: Flat surfaces. Am. J. Math. 115 (1993), 589-689. 23549 Alvise Vitturi: Teoria delle curve algebriche. Tesina 2010, 70p. J. Walker: Codes and curves. AMS 2000, 70p. $15. 4651 Robert Walker: Algebraic curves. Springer 1978. Hermann Weyl: Die Idee der Riemannschen Flaeche. Teubner 1913. 26906 Wikipedia: Riemann-Roch theorem. Internet 2017, 5p. 5208 Scott Wolpert: The topology and geometry of the moduli space of Riemann surfaces. SLN Math. 1111 (1985), 431-451. 22608 Shing-Tung Yau: Geometry of the moduli space of curves. Internet 2007, 58p.