The Minimal Cremona Degree of Quartic Surfaces

Two birational projective varieties in $$\mathbb {P}^n$$ are Cremona Equivalent if there is a modification of mapping one onto the other. The minimal degree $$X\subset \mathbb integer among all degrees that to X. Equivalence and well understood for subvarieties codimension at least 2 while both general very subtle questions divisors. In this note, I compute quartic surfaces {P}^3$$ . This allows me show any surface elliptic ruled type has nontrivial stabilizers group.