A Fano manifold X is a smooth projective

algebraic variety with the ample first Chern class [c.

The Hodge conjecture is a major unsolved problem in the field of algebraic geometry that relates the algebraic topology of a non-singular complex

algebraic variety and the subvarieties of that variety.

In this context, a regulator is a map from the algebraic K-theory of an

algebraic variety to a suitable cohomology theory such as etale cohomology or Deligne cohomology.

Russo, Some remarks on nef and good divisors on an algebraic variety, C.

Russo, On the complement of a nef and big divisor on an algebraic variety, Math.

Put differently: The underlying manifold of an

algebraic variety does not determine these invariants," he added.

It is the purpose of the present paper to investigate the structured distance of a real irreducible tridiagonal matrix to the algebraic variety of real normal irreducible tridiagonal matrices, which we denote by I.

Section 2 introduces notation used throughout the paper, section 3 presents an upper bound for the distance in the Frobenius norm of a real tridiagonal matrix to the algebraic variety of real normal tridiagonal matrices.

Then there exists a proper

algebraic variety V [subset] S st.

We start in Section 2 with the definition of the arc space of an

algebraic variety as the set of formal power series solutions (in one variable) to the defining equations of the variety.

For P in P(r, d), and E an r-filtered bundle on an

algebraic variety (or algebraic scheme) X, by substituting the Chern roots of E for [x.

Finally, we outline (Section 6) an alternative interpretation of the higher critical groups as discrete analogues of the Chow groups of an

algebraic variety.