intersection divisor for a quartic
Let be a non-singular curve in the plane, defined over an algebraically closed field , and given by a polynomial of degree (i.e. is a quartic). Let be a (rational) line in the plane . The intersection divisor of and is of the form:
where , , are points in . There are five possibilities:
The generic position: all the points are distinct.
is tangent to : there exist indices such that . Without loss of generality we may assume and , and .
is bitangent to when and but . It may be shown that if then has exactly bitangent lines.
intersects at exactly two points, thus . The point is called a flex.
intersects at exactly one point and . This point is called a hyperflex. A quartic may not have any hyperflex.
- 1 S. Flon, R. Oyono, C. Ritzenthaler, Fast addition on non-hyperelliptic genus 3 curves, can be found http://eprint.iacr.org/2004/118.pshere.
|Title||intersection divisor for a quartic|
|Date of creation||2013-03-22 15:44:59|
|Last modified on||2013-03-22 15:44:59|
|Last modified by||alozano (2414)|