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1

Horst, Knörrer, ed. Plane algebraic curves. Basel: Birkhäuser Verlag, 1986.

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2

Salmon, George. A treatise on conic sections. 6th ed. Providence, RI: AMS Chelsea Pub., 2005.

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3

Hulek, Klaus. Projective geometry of elliptic curves. Paris: Société Mathématique de France, 1986.

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4

Hulek, Klaus. Projective geometry of elliptic curves. Paris: Socie te Mathe matique de France, 1986.

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5

Ballico, Edoardo, and Ciro Ciliberto, eds. Algebraic Curves and Projective Geometry. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0085918.

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6

Hulek, Klaus. Projective geometry of elliptic curves. Paris: Société mathématique de France, 1986.

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7

The real projective plane. 3rd ed. New York: Springer-Verlag, 1993.

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8

Apéry, François. Models of the real projective plane: Computer graphics of Steiner and Boy surfaces. Braunschweig: Friedr. Vieweg, 1987.

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9

Fowler, R. H. The elementary differential geometry of plane curves. Mineola, N.Y: Dover Publications, 2005.

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10

Shaei kikagaku no kangaekata: An invitation to plane projective geometry. Tōkyō-to Bunkyō-ku: Kyōritsu Shuppan, 2013.

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11

Apéry, François. Models of the real projective plane: Computer graphics of Steiner and Boy surfaces. Braunschweig: Vieweg, 1987.

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12

1960-, Zaslavskiĭ A. A., ed. Geometry of conics. Providence, R.I: American Mathematical Society, 2007.

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13

Zwikker, C. The advanced geometry of plane curves and their applications. Mineola, N.Y: Dover Publications, 2005.

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14

Mumford, David. Algebraic geometry I: Complex projective varieties. Berlin: Springer, 1995.

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15

NURB curves and surfaces: From projective geometry to practical use. Wellesley, Mass: A.K. Peters, 1995.

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16

Porta, Giambattista della. Elementorum curvilineorum libri tres. Napoli: Edizioni scientifiche italiane, 2005.

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17

Lectures on curves, surfaces and projective varieties: A classical view of algebraic geometry. Zürich: European Mathematical Society, 2009.

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18

Geometry: An algebraic approach. Mannheim: BI-Wissenschaftsverlag, 1992.

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19

Vogel, Julia. Crescents. Edina, Minn: Red Wagon, 2008.

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20

Tschinkel, Yuri, Carlo Gasbarri, Steven Lu, and Mike Roth. Rational points, rational curves, and entire holomorphic curves on projective varieties: CRM short thematic program, June 3-28, 2013, Centre de Recherches Mathematiques, Universite de Montreal, Quebec, Canada. Providence, Rhode Island: American Mathematical Society, 2015.

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21

Ovals. New York: Marshall Cavendish Benchmark, 2006.

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22

1946-, Neumann W. D., ed. Three-dimensional link theory and invariants of plane curve singularities. Princeton, N.J: Princeton University Press, 1985.

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23

(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. Providence, R.I: American Mathematical Society, 2012.

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24

1943-, Jha Vikram, and Johnson N. L. 1939-, eds. Foundations of translation planes. New York: Marcel Dekker, 2001.

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25

Intersection and decomposition algorithms for planar arrangements. Cambridge: Cambridge University Press, 1991.

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26

Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View toward Coherent Sheaves (2006 Cambridge, Mass.). Grassmannians, moduli spaces, and vector bundles: Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View towards Coherent Sheaves, October 6-11, 2006, Cambridge, Massachusetts. Edited by Ellwood D. (David) 1966- and Previato Emma. Providence, RI: American Mathematical Society, 2011.

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27

Plane Algebraic Curves. Birkh User, 2012.

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28

Complex Ball Quotients and Line Arrangements in the Projective Plane. Princeton University Press, 2016.

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29

Eagles, T. H. Constructive Geometry Of Plane Curves - Illustrated. Merchant Books, 2007.

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30

Projective differential geometry of curves and ruled surfaces. Leipzig: B. G. Teubner, 1991.

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31

Geometry of Curves (Chapman Hall/Crc Mathematics Series). Chapman & Hall/CRC, 2000.

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32

Campbell, Alan D. Advanced Analytic Geometry. Kessinger Publishing, LLC, 2007.

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33

Eagles, T. H. Constructive Geometry Of Plane Curves: With Numerous Examples. Kessinger Publishing, LLC, 2007.

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34

Eagles, T. H. Constructive Geometry Of Plane Curves: With Numerous Examples. Kessinger Publishing, LLC, 2007.

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35

Apolarität und rationale Curven: Eine systematische Voruntersuchung zu einer allgemeinen Theorie der linearen Räume. Tübingen: F. Fues, 1993.

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36

Chenciner, Alain. Courbes Algébriques Planes. Springer, 2007.

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37

Algebraic curves and projective geometry: Proceedings of the conference held in Trento, Italy, March 21-25, 1988. Berlin: Springer-Verlag, 1989.

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38

Ballico, E. Algebraic Curves and Projective Geometry: Proceedings of the Conference Held in Trento, Italy, March 21-25, 1988 (Lecture Notes in Mathematics). Springer, 1989.

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39

Tretkoff, Paula, and Hans-Christoph Im Hof. Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51). Princeton University Press, 2016.

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40

(Illustrator), Sharon Lane Holm, ed. Crescents (Shapes) (Shapes). Abdo & Daughters, 2007.

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41

Farb, Benson, and Dan Margalit. Curves, Surfaces, and Hyperbolic Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0002.

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This chapter explains the basics of working with simple closed curves, focusing on the case of the closed surface Sɡ of genus g. When g is greater than or equal to 2, hyperbolic geometry enters as a useful tool since each homotopy class of simple closed curves has a unique geodesic representative. The chapter begins by recalling some basic results about surfaces and hyperbolic geometry, with particular emphasis on the boundary of the hyperbolic plane and hyperbolic surfaces. It then considers simple closed curves in a surface S, along with geodesics and intersection numbers. It also discusses the bigon criterion, homotopy versus isotopy for simple closed curves, and arcs. Finally, it describes the change of coordinates principle and three facts about homeomorphisms.
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42

photographer, Weightman Helena, ed. The seduction of curves: The lines of beauty that connect mathematics, art, and the nude. Princeton University Press, 2017.

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43

Borceux, Francis. A Differential Approach to Geometry: Geometric Trilogy III. Springer, 2016.

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44

A Differential Approach to Geometry: Geometric Trilogy III. Springer, 2013.

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45

Géométrie de direction: Application des coordonnées polyédriques. Propriété de dix points de l'ellipsoïde, de neuf points d'une courbe gauche du quatrième ordre, de huit points d'une cubique gauche. Paris: Gauthier-Villars, 1991.

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46

Series, Michigan Historical Reprint. Constructive geometry of plane curves. With numerous examples, by T. H. Eagles. Scholarly Publishing Office, University of Michigan Library, 2005.

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47

An Invitation to Quantum Cohomology: Kontsevich's Formula for Rational Plane Curves (Progress in Mathematics). Birkhäuser Boston, 2006.

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48

Algebraic Curves And Projective Geometry Proceedings Of The Conference Held In Trento Italy March 21 25 1988. Springer, 1989.

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49

Neumann, Walter D., and David Eisenbud. Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110) (Annals of Mathematics Studies). Princeton University Press, 1986.

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50

Kock, Joachim, and Israel Vainsencher. An Invitation to Quantum Cohomology. Springer, 2008.

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