Maximal almost disjoint families, determinacy, and forcing

We study the notion of $\mathcal J$-MAD families where J$ is a Borel ideal on $\omega$. show that if an arbitrary $F_\sigma$ ideal, or any finite countably iterated Fubini product ideals, then there are no analytic infinite families, and assuming Projective Determinacy projective families; under full Axiom + $V=\mathbf{L}(\mathbb{R})$ J$-mad families. These results apply in particular when sets $\mathrm{Fin}$, which corresponds to classical MAD The proofs combine ideas from invariant descriptive set theory forcing.