EQUATIONS OF LINEAR SUBVARIETIES OF STRATA OF DIFFERENTIALS

The paper proves that near any boundary point, a local irreducible component Z of the closure of a linear subvariety is analytically isomorphic to C^n times the zero locus of binomial equations, hence locally toric. Its proof converts linear period equations to plumbing equations via log periods, separates non-horizontal from horizontal contributions, exponentiates to get binomials with unit factors, then absorbs the units by an analytic change of variables and groups variables by M-cross-equivalence classes, yielding a product decomposition; the non-horizontal block is smooth. The candidate solution follows the same steps with the same key ingredients and conclusions. Minor differences are expository (attribution of the log-period formalism) and technical bookkeeping (choice of coordinates/branches), but no substantive conflict.