  Secant defectivity of projective varieties is classically approached via
dimensions of linear systems with multiple base points in general position. The
latter can be studied via degenerations. We exploit a technique that allows
some of the base points to collapse together. We deduce a general result which
we apply to prove a conjecture by Abo and Brambilla: for $c \geq 3$ and $d \geq
3$, the Segre-Veronese embedding of $\mathbb{P}^m\times\mathbb{P}^n$ in
bidegree $(c,d)$ is non-defective.
