(1995) gave a different construction of a quartic with twenty-eight bitangents, formed by projecting a cubic surface; twenty-seven of the bitangents to Shioda's...

a bitangent must have degree at least 4. The case of the 28 bitangents of a quartic was a celebrated piece of geometry of the nineteenth century, a relationship...

exactly one quartic curve that passes through a set of 14 distinct points in general position, since a quartic has 14 degrees of freedom. A quartic curve can...

and internal tangent lines are the bitangents to this quartic curve. A generic quartic curve has 28 bitangents. A third generalization considers tangent...

adjectives were often used as nouns: for example, "quartic" could also be short for "quartic curve" or "quartic surface". In classical algebraic geometry, all...

permutation of the points. These 28 triangles may be viewed as corresponding to the 28 bitangents of a quartic. There are 84 ways of specifying a triangle...

in pairs to the 28 bitangents of a quartic. Degree 3: these are essentially cubic surfaces in P3; the cubic surface is the image of the anticanonical embedding...

curve Bézout's theorem Birch and Swinnerton-Dyer conjecture Bitangent Bitangents of a quartic Cartesian coordinate system Caustic Cesàro equation Chord...

is a degree 60 invariant vanishing on ternary quartics with an inflection bitangent. (Dolgachev 2012, 6.4) The catalecticant of a ternary quartic is the...

on a cubic surface, the 28 bitangents of a plane quartic curve, and the 120 tritangent planes of a canonic sextic curve of genus 4. The first of these...

the remaining 36 of the other; this is basic in the question of counting bitangents, as it corresponds to the 28 bitangents of a quartic. The geometric...

Trott curve, a quartic with four components, are examples of M-curves. This theorem formed the background to Hilbert's sixteenth problem. In a recent development...

z-axis replaces y by (x2 + y2)1/2, and clearing the square root produces a quartic equation for the torus: 0 = ( x 2 + y 2 + z 2 + R 2 − r 2 ) 2 − 4 R 2...

corresponding dual map of Coxeter notation (3,7)8. Other aspects of this work are also cited in the following pages: Bitangents of a quartic. Coxeter graph....

ending in -ic often refer to the degree of a form, as in linear or monic, quadric or quadratic, cubic, quartic or biquadratic, quintic, sextic, septic...

2}(d-1)(d-2).} So, for example, a non-singular quartic plane curve is of genus 3 and has 28 bitangents and 24 points of inflection. Curves are classified...