This paper is devoted to the study of higher secant varieties of varieties of completely decomposable forms. The main goal is to develop methods to inductively verify the non-defectivity of such secant varieties. As an application of these methods, we will establish the existence of large families of non-defective secant varieties of “small” varieties of completely decomposable forms.

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we prove that, given a such variety X which is not exceptional, then X is smooth if and only if an appropriate toric variety contained in X is smooth. keywords:...

Manioc (Manihot esculenta Crantz) originated in Amazonia and is the main staple for more than 800 million people worldwide; it also had a fundamental role as a source of calories for many pre-Columbian peoples, especially in Amazonia, where it was domesticated. There are two major groups of manioc varieties: sweet varieties have low amounts of toxic substances (cyanogenic glycosides) and may be...

The Eastern Himalayan region of Northeast (NE) India is home to a large number of indigenous rice varieties, which may serve as a valuable genetic resource for future crop improvement to meet the ever-increasing demand for food production. However, these varieties are rapidly being lost due to changes in land-use and agricultural practices, which favor agronomically improved varieties. A detail...

The Northeast China (NEC) was the most important agriculture areas and known as the Golden-Maize-Belt. Based on observed crop data and crop model, we design four simulating experiments and separate relative impacts and contribution under climate change, planting date shift, and varieties change as well change of varieties and planting date. Without planting date and varieties change, maize yiel...

This paper develops a new method for studying the cohomology of orthogonal flag varieties. Restriction varieties are subvarieties of orthogonal flag varieties defined by rank conditions with respect to (not necessarily isotropic) flags. They interpolate between Schubert varieties in orthogonal flag varieties and the restrictions of general Schubert varieties in ordinary flag varieties. We give ...

For any type of abstract algebra, a variety is an equationally defined class of such algebras. Recently, attempts have been made to study varieties of lattice-ordered groups (/-groups). Martinez has shown that the set L of all /-group varieties forms a lattice under set inclusion with a compatible associative multiplication. Certain varieties Sp (p prime) have been proved by Scrimger to be mini...

A variety of algebras is a Specht variety if all its subvarieties are finitely based. This article presents the first example of a maximal Specht variety of monoids. The existence of such an example is counterintuitive since it is long known that maximal Specht varieties of semigroups do not exist. This example permits a characterization of Specht varieties in the following four classes based o...

We determine precisely those locally finite varieties of unary algebras of finite type which, when augmented by a ternary discriminator, generate a variety with a decidable theory.

0. Introduction 1 1. Main definitions and results 3 2. General criteria 6 2.1. Seminormality and connectedness of isotropy groups 6 2.2. Finiteness of number of orbits and group–like condition 9 3. Orbits in stable reductive varieties 11 3.1. Isotropy groups 11 3.2. Algebras of regular functions 14 4. Reductive varieties 18 4.1. Classification 18 4.2. Associated stable toric varieties 20 5. Sta...