# Hessian (algebraic curve)

From Encyclopedia of Mathematics

*of an algebraic curve of degree *

The set of points whose conic polars can be split into two straight lines, as well as the set of double points of the first polars. The Hessian of a non-singular curve of degree is a curve of degree and class . If is the equation of a curve of degree in homogeneous coordinates and if , then

is the equation of the Hessian. The Hessian of a non-singular curve of degree 3 in characteristic not equal to three intersects the curve at nine ordinary points of inflection. Named after O. Hesse (1844).

#### Comments

#### References

[a1] | J.L. Coolidge, "A treatise on algebraic plane curves" , Dover, reprint (1959) |

**How to Cite This Entry:**

Hessian (algebraic curve). A.B. Ivanov (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Hessian_(algebraic_curve)&oldid=18385

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098