On grade and formal connectivity for weakly normal varieties

Farmers' perceptions on improved bread wheat varieties and formal seed supply in Ethiopia

The paper presents smallholder farmers' perceptions on attributes of bread wheat varietiesbased on primary data collected from 524 households in four major wheat growing areas ofEthiopia. The results indicated high value of attainment indices for improved varieties comparedto landraces, which shows how the demanded attributes are embodied more in improved ones.Grain yield and yellow and stem ru...

Algebraic Cocycles on Normal, Quasi-Projective Varieties

Blaine Lawson and the author introduced algebraic cocycles on complex algebraic varieties in [FL-1] and established a duality theorem relating spaces of algebraic cocycles and spaces of algebraic cycles in [FL-2]. This theorem has non-trivial (and perhaps surprising) applications in several contexts. In particular, duality enables computations of “algebraic mapping spaces” consisting of algebra...

Normal Varieties and Birational Correspondences

Integral Dependence and Normal Varieties

b + an−1b + · · ·+ a0 = 0. Example 1.2. Let A = Z and B = Q. Then b ∈ Q is integral over Z if and only if b ∈ Z. Indeed, if b ∈ Z then b solves x − b ∈ Z[x]. Conversely, write b = c/d for relatively prime integers c and d, d > 0. Let f(x) = x + an−1x + · · ·+ a0 be a polynomial with integer coefficients that b satisfies. Substituting b for x and multiplying by d we obtain c = −(dan−1c + · · ·+ ...

On weakly e*-open and weakly e*-closed Functions

The aim of this paper is to introduce and study two new classes of functions called weakly $e^{*}$-open functions and weakly $e^{*}$-closed functions via the concept of $e^{*}$-open set defined by Ekici cite{erd1}. The notions of weakly $e^{*}$-open and weakly $e^{*}$-closed functions are weaker than the notions of weakly $beta$-open and weakly $beta$-closed functions defined by Caldas and Nava...