  In part I we reduced the arithmetic (characteristic zero) version of the P
\not \subseteq NP conjecture to the problem of showing that a variety
associated with the complexity class NP cannot be embedded in the variety
associated the complexity class P. We call these class varieties.
  In this paper, this approach is developed further, reducing the nonexistence
problems, such as the P vs. NP and related lower bound problems, to existence
problems: specifically to proving existence of obstructions to such embeddings
among class varieties. It gives two results towards explicit construction of
such obstructions.
  The first result is a generalization of the Borel-Weil theorem to a class of
orbit closures, which include class varieties. The recond result is a weaker
form of a conjectured analogue of the second fundamental theorem of invariant
theory for the class variety associated with the complexity class NC. These
results indicate that the fundamental lower bound problems in complexity theory
are intimately linked with explicit construction problems in algebraic geometry
and representation theory.
