Corollary 1.5. Let be a projective variety of dimension . Suppose has pre--rational singularities (or more generally satisfies condition ), with , and is normal if . Then:
(i) If , then
for all and .
In particular, if , then has weights .
(ii) If , then
for all and .
In particular, if , then has weights .
Entries . Green entries are forced zero by Conjecture 0.5.
Cells marked ✓ have Corollary 1.5 vanishing predictions inside that box; the displayed bound is the Corollary 1.5 cutoff for the Hodge index.
Conjecture 0.5. If is projective and and are nonnegative integers, then we have
if
More precisely, it should suffice to assume
for all , , and .
Required: for all .
Required: for all , , and .