DEEP LOCI OF DOUBLE BOTT–SAMELSON VARIETIES

We prove that the deep locus of a complex double Bott–Samelson variety associated with a positive braid is its stabilizer locus. Consequently, the deep locus is empty if and only if any two components of the braid closure are unlinked. This resolves Conjecture 4.45 of Castronovo, Gorsky, Simental, and Speyer.