  It is well known that there are a great many apparently consistent vacua of
string theory. We draw attention to the fact that there appear to be very few
Calabi--Yau manifolds with the Hodge numbers h^{11} and h^{21} both small. Of
these, the case (h^{11}, h^{21})=(3,3) corresponds to a manifold on which a
three generation heterotic model has recently been constructed. We point out
also that there is a very close relation between this manifold and several
familiar manifolds including the `three-generation' manifolds with \chi=-6 that
were found by Tian and Yau, and by Schimmrigk, during early investigations. It
is an intriguing possibility that we may live in a naturally defined corner of
the landscape. The location of these three generation models with respect to a
corner of the landscape is so striking that we are led to consider the
possibility of transitions between heterotic vacua. The possibility of these
transitions, that we here refer to as transgressions, is an old idea that goes
back to Witten. Here we apply this idea to connect three generation vacua on
different Calabi-Yau manifolds.

High Energy Physics - Theory;Astrophysics;High Energy Physics - Phenomenology;Algebraic Geometry