  In this paper, we study the variety of all nonassociative (NA) algebras from
the idempotent point of view. We are interested, in particular, in the spectral
properties of idempotents when algebra is generic, i.e. idempotents are in
general position. Our main result states that in this case, there exist at
least $n-1$ nontrivial obstructions (syzygies) on the Peirce spectrum of a
generic NA algebra of dimension $n$. We also discuss the exceptionality of the
eigenvalue $\lambda=\frac12$ which appears in the spectrum of idempotents in
many classical examples of NA algebras and characterize its extremal properties
in metrised algebras.
