diff --git a/projective_hodge_iitaka_v2.txt b/projective_hodge_iitaka_v2.txt
index e923e83..b8307e4 100644
--- a/projective_hodge_iitaka_v2.txt
+++ b/projective_hodge_iitaka_v2.txt
@@ -3,6 +3,14 @@ PROJECTIVE HODGE LINES AND ORDINARY IITAKA SUBADDITIVITY
 
 A complete proof, written to be read from the beginning.
 
+ABSTRACT
+
+We prove the ordinary Iitaka subadditivity conjecture for surjective
+projective morphisms with connected fibers between smooth connected
+projective varieties over algebraically closed fields of characteristic
+zero.  If F is the geometric generic fiber of f : X -> Z, then
+kappa(X) >= kappa(F) + kappa(Z).
+
 
 CONTENTS
 
@@ -26,6 +34,18 @@ CONTENTS
   References
 
 
+READER'S GUIDE
+
+A reader new to the subject should start with Sections 0-2: the
+theorem in plain words, the language, and the strategy on one page.
+From there, Section 9 assembles the whole proof assuming the technical
+steps of Sections 3-8, so a first-time reader can go straight from
+Section 2 to Section 9 to see the shape, and only then dive into the
+technical preparation.  Sections 3-8 are the heart, proving adjoint
+positivity (Theorem 3.1).  Sections 10 and 11 give alternate proofs
+of that step and can be skipped on a first pass.
+
+
 0. THE THEOREM, IN PLAIN WORDS
 
 Fix once and for all an algebraically closed field k of characteristic
@@ -94,6 +114,10 @@ integer between 0 and dim V.  Equivalently (and this equivalence is
 the definition used in proofs), H^0(V, m K_V) grows like m^kappa(V)
 once m is large.
 
+A first concrete picture comes from smooth projective curves.  There
+kappa(C) = -infinity for the projective line, kappa(C) = 0 for an
+elliptic curve, and kappa(C) = 1 for every curve of genus at least two.
+
 Two features matter here:
 
   - The conventions (-infinity) + a = -infinity and kappa(point) = 0.
@@ -135,6 +159,12 @@ connection sends F^p into F^{p-1} hat O.  This is the horizontal
 character of Hodge theory: the filtration may only move "downwards"
 by one degree.
 
+The filtration is bookkeeping for the finer decomposition.  At every
+point the fibre V breaks into a direct sum of Hodge pieces V^{a,b}
+with a + b = w, and the subbundle F^p is the sum of those pieces with
+a >= p.  In particular F^w is H^{w,0}, the space of holomorphic
+w-forms, and F^p = 0 for p > w.
+
 The period domain D is the set of all Hodge filtrations of the type
 fixed by (2); it is a complex manifold on which the orthogonal group
 of Q acts.  On the universal cover of U, a flat trivialization of V
@@ -164,6 +194,12 @@ which F^p is not zero.  Suppose this top piece F^m is a line bundle
 (rank one).  We call it the highest Hodge line, or just the Hodge line,
 and write J for its first Chern class once it has been extended.
 
+A concrete case to keep in mind: a family of K3 surfaces.  On H^2 of
+each fibre there is a weight-2 variation, and its top piece F^2 =
+H^{2,0} is one-dimensional, so this variation has a highest Hodge
+line.  A family of elliptic curves does the same one degree lower,
+where F^1 = H^{1,0} is the line.
+
 On a simply connected patch, choose a flat frame for V.  Then the line
 F^m becomes a holomorphic map
 
@@ -289,7 +325,11 @@ is -infinity by convention and there is nothing to prove.  So assume
 kappa(F) = d >= 0 and kappa(Z) >= 0.
 
 Step 1 (Section 8).  Run the relative Iitaka fibration of f.  This
-produces a birational model of X sitting over a new variety Y:
+replaces the fibre F by its own Iitaka fibration, absorbing the
+kappa(F)-dimensional part into a new base Y; the remaining fibres of
+g: X~ -> Y are then Kodaira-dimension-zero, a far simpler case.
+Concretely, it produces a birational model of X sitting over a new
+variety Y:
 
       X~  --g-->  Y  --q-->  Z,     dim(Y/Z) = d,