F-structures and integral points on semiabelian varieties over finite fields

Motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields, we prove a quantifier elimination result for certain modules over finite simple extensions of the integers given together with predicates for orbits of the distinguished generator of the ring.Comment: 33 pages, correction made to authors' informatio

Susceptibility to Apple Scab, Nectria Cancer and Powdery Mildew of Different Unsprayed Apple Varieties

Twentyfive apple varieties were evaluated for Apple scab (Venturia inaqualis), Nectria canker (Nectria galligena) and Powdery mildew (Podosphaera leucotricha) for 4 to 7 years. The trees were grown unsprayed. The weather conditions at the experimental orchard normally results in high infections of apple scab and low infections of powdery mildew. Infections of Apple scab is often seen also in scab resistant varieties. Williams Pride, Katinka and Katrina (scabresistant varieties) were the only varieties not showing scab in the experimental period. The two scabresistant varieties Angold and Produkta (varieties having a poor fruit quality) was unsusceptible to Nectria canker. The reference variety Elstar/Elshof was in all plantings among the most resistant varieties. Powdery mildew is not a problem at the experimental orchard. Most varieties had low susceptibility to Powdery mildew. Varieties with low susceptibility to diseases in general were Angold, Produkta, Rajka, Rubinola, Ahrista, Gerlinde, Gul Richard, Sukkertop, Katinka, Katrina, Marian and Primicia

Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1

Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional $F_4$-homogeneous manifold associated to a short simple root.Comment: 22 page