TWELVE POINTS ON THE PROJECTIVE LINE, BRANCHED COVERS, AND RATIONAL ELLIPTIC FIBRATIONS RAVI VAKIL Abstract. The following divisors in the space Sym12 P1 of twelve points on P1 are actually the same: (A) the possible loc

Source URL: math.stanford.edu

• Algebraic surfaces
• Algebraic curves
• Birational geometry
• Vector bundles
• Canonical bundle
• Elliptic surface
• Del Pezzo surface
• Ample line bundle
• Riemann–Roch theorem
• Algebraic geometry
• Geometry
• Abstract algebra

TWISTS OF X(7) AND PRIMITIVE SOLUTIONS TO x2 + y 3 = z 7 BJORN POONEN, EDWARD F. SCHAEFER, AND MICHAEL STOLL Abstract. We find the primitive integer solutions to x2 + y 3 = z 7 . A nonabelian descent argument involving t

Source URL: math.mit.edu

• Algebraic curves
• Group theory
• Algebraic number theory
• Elliptic curve
• J-invariant
• Algebraic number field
• Modular curve
• Μ operator
• Classical modular curve
• Abstract algebra
• Analytic number theory
• Modular forms

Complete Subdivision Algorithms, I: Intersection of Bezier Curves ∗ Chee K. Yap

Source URL: www.cs.nyu.edu

• Elliptic curves
• Algebraic curve
• Algebraic geometry
• Curve
• Intersection number
• Intersection theory
• Ample line bundle
• Counting points on elliptic curves
• Abstract algebra
• Geometry
• Mathematics

Computing elliptic curves using KASH Masanari K University of Electro-Communications e-mail: [removed] August 18, 2002 Beijing, China

Source URL: matha.e-one.uec.ac.jp

• Algebraic number theory
• Analytic number theory
• Elliptic curve
• Group theory
• Elliptic functions
• Modular forms
• KANT
• J-invariant
• Algebraic number field
• Abstract algebra
• Algebra
• Mathematics

1 A Note on Scalar Multiplication Using Division Polynomials Binglong Chen, Chuangqiang Hu and Chang-An Zhao

Source URL: eprint.iacr.org

• Elliptic curves
• Group theory
• Finite fields
• Number theory
• Cryptography
• Elliptic divisibility sequence
• Division polynomials
• Hyperelliptic curve cryptography
• Supersingular elliptic curve
• Algebra
• Abstract algebra
• Mathematics

A TOOL FOR STABLE REDUCTION OF CURVES ON SURFACES RAVI VAKIL Abstract. In the study of the geometry of curves on surfaces, the following question often arises: given a one-parameter family of divisors over a pointed

Source URL: math.stanford.edu

• Moduli theory
• Vector bundles
• Analytic number theory
• Elliptic curve
• Group theory
• Intersection number
• Curve
• Divisor
• Moduli space
• Abstract algebra
• Geometry
• Algebraic geometry

THE ENUMERATIVE GEOMETRY OF RATIONAL AND ELLIPTIC CURVES IN PROJECTIVE SPACE RAVI VAKIL Abstract. We study the geometry of moduli spaces of genus 0 and 1 curves in Pn with specified contact with a hyperplane H. We comput

Source URL: math.stanford.edu

1 An Improvment of the Elliptic Net Algorithm Binglong Chen and Chang-An Zhao* Abstract In this paper we propose a modified Elliptic Net algorithm to compute pairings. By reducing the number of the

Source URL: eprint.iacr.org

• Cryptography
• Elliptic curves
• Finite fields
• Group theory
• Analytic number theory
• Pairing
• Elliptic curve cryptography
• Elliptic curve
• Weil pairing
• Abstract algebra
• Algebra
• Mathematics

New algorithm for the discrete logarithm problem on elliptic curves Igor Semaev Department of Informatics University of Bergen, Norway e-mail: [removed]

Source URL: eprint.iacr.org

Proceedings of 7th G¨ okova Geometry-Topology Conference, pp, 1 – 7 On the tautological ring of Mg,n

Source URL: math.stanford.edu

• Moduli theory
• Algebraic curves
• Invariant theory
• Moduli space
• ELSV formula
• Moduli of algebraic curves
• Hyperelliptic curve
• Elliptic curve
• Chow ring
• Algebraic geometry
• Abstract algebra
• Geometry