Website: www.math.ucsd.edu/~funconf/SLIDES/sturmfels.pdf

A quartic is an algebraic curve of degree 4.
Most of the remarkable quartics of this encyclopaedia are rational (i.e. of genus zero), but a quartic can be:
    - elliptic (i.e. of genus 1, like the Cartesian curves, the plane spirics, the polyzomal curves, the conchals)
    - of genus 2 (like the devil's curve)
    - or of genus 3, when they are smooth (like the Klein quartic, the Plücker quartic, the Salmon quartic, or the Loriga quartic).

For more examples, see bicircular quartic.
 

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© Robert FERRÉOL  2017