fixup: correct comments for twistedGlobalSectionsModule and cohomology

M2/Macaulay2/m2/varieties.m2

@@ -369,13 +369,13 @@ twistedGlobalSectionsModule = (F, bound) -> (
     -- TODO: both n and w need to be adjusted for the multigraded case
     N := flattenModule M;
     S := ring N;
-    n := dim S;
-    w := S^{-n}; -- canonical sheaf on P^n
+    n := dim S-1;
+    w := S^{-n-1}; -- canonical sheaf on P^n
     -- Note: bound=infinity signals that H_m^1(M) = 0, ie. M is saturated
     -- in other words, don't search for global sections not already in M
-    -- TODO: what would pdim N < n-1, hence E1 = 0, imply?
-    if bound < infinity and pdim N >= n-1 then (
-	E1 := Ext^(n-1)(N, w); -- the top Ext
+    -- TODO: what would pdim N < n, hence E1 = 0, imply?
+    if bound < infinity and pdim N >= n then (
+	E1 := Ext^n(N, w); -- the top Ext
 	p := (
 	    if dim E1 <= 0 -- 0-module or 0-dim module
 	    then 1 + max degreeList E1 - min degreeList E1
@@ -426,12 +426,12 @@ cohomology(ZZ, ProjectiveVariety, CoherentSheaf) := Module => opts -> (p, X, F)
 	M := flattenModule module F;
 	A := ring M;
 	-- TODO: both n and w need to be adjusted for the multigraded case
-	n := dim A;
-	w := A^{-n};
+	n := dim A-1;
+	w := A^{-n-1};
 	-- using Serre duality for coherent sheaves on schemes with mild
 	-- singularities, Cohen–Macaulay schemes, not just smooth schemes.
 	-- TODO: check that X is proper (or at least finite type)
-	Ext^(n-1-p)(M, w));
+	Ext^(n-p)(M, w));
     k := coefficientRing ring F;
     F.cache.HH#p = k^(rank source basis(0, G)))