diff --git a/projective_hodge_iitaka_v2.txt b/projective_hodge_iitaka_v2.txt
index f59a4a4..fa849dd 100644
--- a/projective_hodge_iitaka_v2.txt
+++ b/projective_hodge_iitaka_v2.txt
@@ -18,47 +18,6 @@ kappa(X) >= kappa(F) + kappa(Z).
 
 
 
-0. THE THEOREM, IN PLAIN WORDS
-
-Fix once and for all an algebraically closed field k of characteristic
-zero (for example the complex numbers).  Let
-
-      f : X -> Z
-
-be a surjective morphism of smooth connected projective varieties over
-k with connected fibers.  Think of X as a family of varieties
-F_z = f^{-1}(z) parametrized by the base Z.  The "geometric generic
-fiber" F is the fiber over a point of Z that is as general as possible.
-
-The theorem is:
-
-   kappa(X) >= kappa(F) + kappa(Z).
-
-Here kappa is the Kodaira dimension.  Roughly, kappa(V) measures how
-fast the space of pluricanonical forms on V grows with the degree, and
-it lies in {-infinity, 0, 1, ..., dim V}.  The inequality says the
-complexity of the total family is at least the complexity of a fibre
-plus the complexity of the base.  This is Iitaka's subadditivity
-conjecture in the "ordinary" (no boundary divisor) case, and we prove
-it in full below.
-
-Three big inputs drive the proof:
-
-  (A) a positivity theorem for a single line of a variation of Hodge
-      structure (the "highest Hodge line");
-  (B) the canonical bundle formula, which converts the geometry of f
-      into a pair (Y, B) and a nef divisor M on a smaller base;
-  (C) log-general-type-fiber subadditivity (Kovacs-Patakfalvi,
-      Hashizume) together with Fujino's weak positivity.
-
-The genuinely new content is (A): proving that the Hodge line M is
-positive in the precise sense needed.  Everything else assembles (A)
-with (B) and (C).  The appendices (Sections 10 and 11) give two other
-proofs of (A); the main text proves (A) in Sections 3-7.
-
------
-
-
 1. BACKGROUND
 
 This section states, in words, everything the proof uses.  The two