Invariants of hypersurface singularities in positive characteristic (Q365156)

Let \(K\) be an algebraically closed field of arbitrary characteristic and \(f\in \langle x_1, \dots, x_m\rangle ^2 K[x_1, \dots, x_n]\). Improved bounds for the degree of determinancy of \(f\) in positive characteristic are given. If \(\mu(f)<\infty \) then the right determinancy of \(f\) is at most \(2\mu(f)-\text{ord}(f)+2\). If \(\tau(f)<\infty\) then the contact determinancy of \(f\) is at most \(2\tau(f)-\text{ord}(f)+2\). Here \(\mu\) respectively \(\tau\) is the Milnor (resp. Tjurina) number. Different non-degeneracy conditions of Kouchnirenko, Wall and Beelen--Pellikaan type are studied. Especially it is proved that planar Newton non-degenerate singularities satisfy \(\mu=2\delta -r+1\).