diff --git a/projective_hodge_iitaka_v2.txt b/projective_hodge_iitaka_v2.txt
index c38fbb2..d38ca54 100644
--- a/projective_hodge_iitaka_v2.txt
+++ b/projective_hodge_iitaka_v2.txt
@@ -686,7 +686,7 @@ preserving the lattice and polarization and covering the action.  Put
 the effective group on T; keep H for the action on V (its kernel on T
 may act nontrivially on fibres).  Fix a connected period domain D and a
 neat arithmetic group Gamma' containing the monodromy, and let
-phi : U_N -> Gamma' \ D be the full period map.  Assume the
+phi : U_N -> Gamma' minus D be the full period map.  Assume the
 normalization B of the closure of its actual image is algebraic, that
 T dash-> B is birational, and that phi is generically immersive; in
 particular C(T) = C(B).
@@ -743,7 +743,7 @@ Suppose nu(J|_E) >= r.  The rank on E is at most r because all
 (r+1)-minors of the extending line map vanish by continuation, so it
 equals r.  Lemma 5.4, with N = 0, puts a nonempty open set of top lines
 in ker(a - lambda); Lemma 4.3 then shows a preserves every full period,
-so x(by) = x(y).  Projecting to Gamma' \ D gives phi(by) = phi(y) on a
+so x(by) = x(y).  Projecting to Gamma' minus D gives phi(by) = phi(y) on a
 nonempty open set.  Since B is the normalization of the actual image,
 its map is birational, hence injective over a dense open subset of that
 image, and b acts trivially on C(B).  The chosen model has
@@ -828,7 +828,7 @@ isometries of D; it contains the monodromy.  Let Gamma' be a normal
 neat subgroup of finite index.  The kernel of pi_1(U) -> Gamma/Gamma'
 defines a connected finite Galois cover U' -> U with deck group H.
 The period map of V|U' factors through B = normalization of the closure
-of its actual image in Gamma' \ D; B is normal quasiprojective and its
+of its actual image in Gamma' minus D; B is normal quasiprojective and its
 period realization is generically immersive (Bakker-Brunebarbe-
 Tsimerman).  We do NOT replace B by its relative algebraic closure.
 
@@ -1270,7 +1270,7 @@ p_1^{-1}(U) of kl(K_{Y_1/S_1}+B_1) + beta p_1^*A.  The big divisor
 kl sigma*P - beta A = kl(sigma*P - A/(k alpha)) has an effective
 multiple; multiply to get a nonzero section over p_1^{-1}(U) of a
 multiple of D_1 = K_{Y_1/S_1}+B_1+p_1^*sigma^*P, with poles only above
-S_1 \ U.  So there are n>0, rational phi != 0, and effective
+S_1 minus U.  So there are n>0, rational phi != 0, and effective
 mu-exceptional T with div(phi) + n D_1 + T >= 0.  Put D_0 = K_{Y/S}+B+
 p*P, R = K_{S_1} - sigma*K_S >= 0; then D_1 = mu*D_0 + E - p_1^*R.  Push
 forward to the smooth Y using mu_*E = mu_*T = 0:
@@ -1478,7 +1478,7 @@ satisfies the condition of Lemma 10.4.  If A_1 is its top Hodge
 extension then b pi* L ~Q h* A_1 for h : P~ -> Z with connected fibres.
 
 Proof.  The full period map factors through an algebraic dominant
-P^o -> Y_0 with Y_0 -> Gamma_ar \ D a closed analytic immersion (Bakker-
+P^o -> Y_0 with Y_0 -> Gamma_ar minus D a closed analytic immersion (Bakker-
 Brunebarbe-Tsimerman).  Normalize Y_0 in the relative algebraic closure
 of C(Y_0) in C(P); this is finite and leaves C(Y_0) relatively
 algebraically closed, so the generic fibre is geometrically connected.