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Plane curve
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61	Math 255: Algebraic Curves Bernd Sturmfels, UC Berkeley, Fall 2011 Homework # 5, due Tuesday, November[removed]Fulton[removed]Fix a DVR R with quotient field K and maximal ideal m. (a) Show that if z ∈ K\R then z −1 ∈ Add to Reading List Source URL: math.berkeley.edu Language: English - Date: 2011-10-13 10:43:57 Algebraic curves Linear system of divisors Divisor Curve Quartic plane curve Intersection number Local parameter Algebraic geometry Abstract algebra Geometry
62	Duality of Plane Curves Maria Monks December 1, 2011 Abstract The dual of an algebraic curve C in RP2 defined by thepolynomial equation f (x, y, z) = Add to Reading List Source URL: math.berkeley.edu Language: English - Date: 2012-06-01 14:02:56 Duality Homogeneous coordinates Projective space Pole and polar Real projective plane Conic section Algebraic curve Projective plane Cubic plane curve Geometry Projective geometry Dual curve
63	Master’s thesis, defended on June 20, 2007, supervised by Dr. Oleg Karpenkov Valerio Pastro Construction of Rational Elliptic Surfaces Add to Reading List Source URL: www.math.leidenuniv.nl Language: English - Date: 2010-07-10 16:11:02 Algebraic surfaces Diophantine geometry Birational geometry Elliptic curves Algebraic curves Elliptic surface Mordell–Weil theorem Cubic plane curve Abelian variety Algebraic geometry Abstract algebra Geometry
64	A Generalization of the Nagel Point1 Avni Pllana In Fig. 1 is shown an arbitrary triangle ABC. Let angle(CAY) = angle(BAZ) = theta , angle(ABZ) = angle(CBX) = phi , angle(BCX) = angle(ACY) = psi . Points Pa, Pb, Pc repre Add to Reading List Source URL: trisectlimacon.webs.com Language: English Incircle and excircles of a triangle Triangle center Euler line Circumscribed circle Triangle De Longchamps point Barycentric coordinate system Cubic plane curve Pedal triangle Geometry Triangle geometry Triangles
65	BRAID MONODROMY INVARIANTS OF PLANE ALGEBRAIC, HURWITZ, AND SEMI–ALGEBRAIC CURVES Vik. S. Kulikov Let C ⊂ CP2 be a plane algebraic curve of degree deg C = d. The embedding C ⊂ CP2 is determined, up to diffeotopy, b Add to Reading List Source URL: www.liv.ac.uk Language: English - Date: 2002-05-24 12:44:14 Complex analysis Riemann surfaces Group theory Algebraic topology Monodromy Braid group Algebraic curve Branch point Curve Mathematical analysis Abstract algebra Topology
66	The Math Circle, Spring[removed]Talks by Gordon Ritter) What is Non-Euclidean Geometry? Most geometries on the plane R2 are non-Euclidean. Let s denote arc length. Then Euclidean geometry arises from the formula for curve Add to Reading List Source URL: www.themathcircle.org Language: English - Date: 2007-02-16 09:21:01 Coordinate systems Integral calculus Multivariable calculus Differential geometry Polar coordinate system Cylindrical coordinate system Arc length Curvature Pythagorean theorem Geometry Mathematical analysis Mathematics
67	MATH CIRCLE - ELLIPTIC CURVES WEEKS 1 & 2 SAM LICHTENSTEIN 1. What is a curve? We started by considering the idea of a curve. This is just the set of points in the plane which satisfy a polynomial equation. For example, Add to Reading List Source URL: www.themathcircle.org Language: English - Date: 2007-10-20 22:29:22 Algebraic curves Diophantine equations Analytic number theory Elliptic curve Group theory Rational point Rational number Curve Infinite descent Mathematics Geometry Abstract algebra
68	THREE NEW FACTORS OF FERMAT NUMBERS R. P. BRENT, R. E. CRANDALL, K. DILCHER, AND C. VAN HALEWYN Abstract We report the discovery of a new factor for each of the Fermat numbers F13 , F15 , F16 . These new factors have 27, Add to Reading List Source URL: gan.anu.edu.au Language: English - Date: 2003-11-05 11:07:22 Integer sequences Integer factorization algorithms Euclidean plane geometry Fermat number Number theory Pierre de Fermat Lenstra elliptic curve factorization Integer factorization Richard P. Brent Mathematics Abstract algebra Group theory
69	MATH CIRCLE - ELLIPTIC CURVES WEEK 4 SAM LICHTENSTEIN This week we picked up where we left off regarding the use of so-called homogeneous coordinates on the projective plane instead of ordinary coordinates on the ordinar Add to Reading List Source URL: www.themathcircle.org Language: English - Date: 2007-11-02 22:35:37 Cubic plane curve Projective plane Elliptic curve Real projective plane Projective space Geometry Projective geometry Homogeneous coordinates
70	Elliptic curves, their companions, and their statistics Barry Mazur What is the probability that a cubic plane curve with rational coefficients has infinitely many rational points? Questions of this type (more exactly fo Add to Reading List Source URL: www.math.harvard.edu Language: English - Date: 2011-12-13 10:36:46 Diophantine geometry Elliptic curves Abelian varieties Analytic number theory Group theory Mordell–Weil theorem Rational point Arithmetic of abelian varieties Curve Abstract algebra Mathematics Algebraic geometry

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