The boundary of linear subvarieties

We describe the boundary of linear subvarieties in moduli space multi-scale differentials. Linear are algebraic strata (possibly) meromorphic differentials that local period coordinates given by equations. The main example such affine invariant submanifolds, is, closures $\operatorname{SL}(2,\mathbb{R})$-orbits. prove any subvariety is again equations generalized boundary. Our technical tool an asymptotic analysis periods near which yields further techniques and results independent interest.