Introduction 1 1. Kanev’s construction and Prym-Tyurin varieties of E6-type 7 2. The E6 lattice 11 3. Degenerations of Jacobians and Prym varieties 13 4. Degenerations of Prym-Tyurin-Kanev varieties 15 5. The global geometry of the Hurwitz space of E6-covers 20 6. The Prym-Tyurin map along boundary components of Hur 30 7. Ordinary Prym varieties regarded as Prym-Tyurin-Kanev varieties 39 8. The...

Sweet potato (Ipomoea batatas) is one of the stable tuber crops consumed by many households in Nigeria. It can be found in different varieties and exist in many colours of skin and flesh. The production of this important crop is still very low, thereby compromising food security. Sweet potato is one of the target commodity crops under the Nigerian Agriculture Sector Investment Opportun...

Among all complex projective varieties X →֒ P(V ), the equivarient embeddings of homogeneous varieties—those admitting a transitive action of a semi-simple complex algebraic group G—are the easiest to study. These include projective spaces, Grassmannians, non-singular quadrics, Segre varieties, and Veronese varieties. In Joe Harris’ book “Algebraic Geometry: A First Course” [H], he computes the ...

In this paper, we study the analogue of the Shafarevich conjecture for polarized Calabi-Yau varieties. We use variations of Hodge structures and Higgs bundles to establish a criterion for the rigidity of families. We then apply the criterion to obtain that some important and typical families of Calabi-Yau varieties are rigid, for examples., Lefschetz pencils of Calabi-Yau varieties, strongly de...

We give some bounds on the numbers of rational points on abelian varieties and jacobians varieties over finite fields. The main result is that we determine the maximum and minimum number of rational points on jacobians varieties of dimension 2.

Using Margulis’s results on lattices in semisimple Lie groups, we prove the GrothendieckKatz p-Curvature Conjecture for many locally symmetric varieties, including HilbertBlumenthal modular varieties and the moduli space of abelian varieties Ag when g > 1.

We explain a technical result about p-adic cohomology and apply it to the study of Shimura varieties. The technical result applies to algebraic varieties with torsion-free cohomology, but for simplicity we only treat abelian varieties.

The most important tool for classifying recognizable languages is Eilenberg’s variety theorem [1], which gives a one-to-one correspondence between (pseudo)-varieties of finite semigroups and varieties of recognizable languages. Varieties of recognizable languages are classes of recognizable languages closed under union, intersection, complement, left and right quotients and inverse morphisms. R...

Some Swedish spring wheat varieties have recently been shown to carry a rare wildtype (wt) allele of the gene NAM-B1, known to affect leaf senescence and nutrient retranslocation to the grain. The wt allele is believed to increase grain protein concentration and has attracted interest from breeders since it could contribute to higher grain quality and more nitrogen-efficient varieties. This stu...

OBJECTIVE Varieties of red raw rice are widely believed to have a better nutritional quality. The physiological effects of consuming different varieties of rice may not be so. The glycaemic index has been developed as an indicator of the physiological effect of foods. It is the glycaemic response of a 50 g carbohydrate portion of food expressed as a percentage of that of a standard. The objecti...