Essential dimension of cubics

In this paper, we compute the essential dimension of the functor of cubics in three variables up to linear changes of coordinates when the base field has characteristic different from 2 and 3. For this, we use canonical pencils of cubics, Galois descent techniques, and the basic material on essential dimension developed in [G. Berhuy, G. Favi, Doc. Math. 8 (2003) 279–330] which is based on Merkurjevʹs notes [Essential dimension, 1999].