This investigation examined the efficiency of various screening procedures which could be used in breeding for increased production of root-proliferating (RP) genotypes of alfalfa (Medicago sativa L. s. l.). Also investigated were relationships between RP and winter growth characteristics in populations derived from crosses between dormant, RP clones and nondormant, non-RP clones. In addition, this investigation also considered the inheritance of the RP habit. Plants from an 11-month F₁ progeny test containing 3508 offspring were qualitatively analyzed for RP expression using three pairs of screening procedures. Procedures compared included: (1) direct-seeding vs. transplanting; (2) use of characterized parental clones (known RP-expressing genotypes selected from field nursery) vs. uncharacterized parental clones (genotypes derived from RP seed lots with no prior knowledge of their ability to express the RP habit) in RP x nondormant crosses; and (3) low vs. high harvest frequencies. A low frequency (3.3%) of F₁ plants exhibited adventitious shoot formation. No differences were observed in the frequency of RP-expressing genotypes between the direct-seeded and transplanted treatments or between the low and high harvest frequency treatments. Characterized RP parents produced a hybrid population with a significantly higher frequency of RP-expressing genotypes than did the F₁ population derived from uncharacterized RP parents. Average winter forage production of the F₁ hybrids were similar in magnitude to the midparent value. Plant height was significantly and positively correlated with forage yield and could be used as an accurate indicator of winter forage yield in analyses of RP segregants. Estimates of components of genetic variance for RP expressivity indicated a predominance of additive effects and narrow sense heritability of 8.4%. Family selection and progeny testing are suggested for maximum breeding progress.

Yields of Washington Navel orange [Citrus sinensis (L.) Osbeck] under Arizona desert conditions are low, due mostly to a low number of harvested fruit and secondly to small sized fruits. To determine at which development stage yield reduction occurred, flowering branches were tagged at mid-bloom and the leaves and flowers were counted. The percent flowers shed at certain times was then recorded. In addition, 27 years yield data for the Arizona-California and Central California production regions were examined in relation to temperature and relative humidity to identify factors causing low yields in the desert climate. It was found that a low number of fruit was due to a low percentage fruit set, while fruit shedding during June drop contributed somewhat less to reducing the number of harvested fruits. A lower percentage of fruits were lost from Arizona Navel orange trees during and after June drop than reported for trees in Florida and California. This resulted in a higher percentage of initial flowers becoming mature fruit, even though there were fewer harvested fruits per tree in Arizona. It was concluded that Navel orange trees growing in Arizona have relatively fewer flowering branches. A correlation between yields and temperatures for 27 years showed that mean and maximum temperatures during the period from June prior to flowering through June after flowering had a highly significant, adverse effect on yields of Arizona grown trees, but not on yields of California grown trees. Relative humidity had no observable effect on yield. In addition, low yields of Navel orange trees in Arizona was disassociated with soil salinity. Low leaf to flower ratios (L/F) had a significant effect on fruit set only if L/F was 1.0 or less. However, the effects of L/F were insignificant to the number of harvested fruits. Foliar applications of potassium nitrate (KNO₃) for two successive years significantly increased yield. Gibberellic acid (GA₃) did not increase fruit set and harvested yields. Benzyladenine (BA) combined with overhead sprinklers failed to reduce the number of fruit shed during June drop. Transpiration and photosynthesis rates for both Navel and Valencia orange trees were low under Arizona conditions.

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This thesis is comprised of three logically independent parts. As the title suggests, each part is related to vector bundles on abelian varieties. We first use Brill-Noether theory to study the geometry of a general curve in its canonical embedding. We prove that there is no $g$ for which the canonical embedding of a general curve of genus $g$ lies on the Segre embedding of any product of three or more projective spaces. We then consider non-degenerate line bundles on abelian varieties. Central to our work is Mumford's index theorem. We give an interpretation of this theorem, and then prove that non-degenerate line bundles, with nonzero index, exhibit positivity analogous to ample line bundles. As an application, we determine the asymptotic behaviour of families of cup-product maps. Using this result, we prove that vector bundles, which are associated to these families, are asymptotically globally generated. To illustrate our results, we consider explicit examples. We also prove that simple abelian varieties, for which our results apply in all possible instances, exist. This is achieved by considering a particular class of abelian varieties with real multiplication. The final part of this thesis concerns the theory of theta and adelic theta groups. We extend and refine work of Mumford, Umemura, and Mukai. For example, we determine the structure and representation theory of theta groups associated to a class of vector bundles which we call simple semi-homogeneous vector bundles of separable type. We also construct, and clarify functorial properties enjoyed by, adelic theta groups associated to line bundles. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-06-24 17:14:21.687

This thesis extends Tate’s conjectures from the smooth case to quotient varieties. It shows that two of those conjectures hold for quotient varieties if they hold for smooth projective varieties. We also consider arbitrary product of modular curves and show that the three conjectures of Tate (in codimension 1) hold for this product. Finally we look at quotients of the surface V = X1(N)×X1(N) and prove that Tate’s conjectures are satisfied for those quotients. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-09-21 09:43:47.789

Call number: LD2668 .T4 1950 G66 / Master of Science

The thesis consists of four chapters. First chapter is introductory. In Chapter 2, we recall some basic facts from the singularity theory of algebraic varieties (see Section 2.2) and the theory of minimal models (see Section 2.3), which will be used throughout the rest of the thesis. We also make some conventions on the notions and notation used in the thesis (see Section 2.1). Each Chapter 3 and 4 starts with some preliminary results (see Sections 3.1 and 4.1, respectively). Each Chapter 3 and 4 ends with some corollaries and conclusive remarks (see Sections 3.7 and 4.4, respectively). In Chapter 3, we prove Theorem 1.2.7, providing the complete description of Halphen pencils on a smooth projective quartic threefold X in P4. Let M be such a pencil. Firstly, we show that M ⊂ | − nKX | for some n ∈ N, and the pair (X,1n M) is canonical but not terminal. Further, if the set of not terminal centers CS(X, 1 ) (see Remark 2.2.8) does not contain points, we show that n = 1 (see Section 3.2). Finally, if there is a point P ∈ CS(X, n M), in Section 3.1 we show first that a general M ∈ M has multiplicity 2n at P (cf. Example 1.2.3). After that, analyzing the shape of the Hessian of the equation of X at the point P , we prove that n = 2 and M coincides with the exceptional Halphen pencil from Example 1.2.6 (see Sections 3.3-3.6). In Chapter 4, we prove Theorem 1.2.11, which shows, in particular, that a general smooth K3 surfaces of type R is an anticanonical section of the Fano threefold X with canonical Gorenstein singularities and genus 36. In Section 4.2, we prove that X is unique up to an isomorphism and has a unique singular point, providing the geometric quotient construction of the moduli space F in Section 4.3 (cf. Remark 1.2.12). Finally, in Section 4.3 we prove that the forgetful map F −→ KR is generically surjective.

Yu, Hok Pun. / Thesis submitted in: October 2008. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 55-56). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Complex Tori --- p.8 / Chapter 2.1 --- Homomorphisms of complex tori --- p.9 / Chapter 2.2 --- Cohomology of Complex Tori --- p.10 / Chapter 3 --- Line bundles on complex tori --- p.11 / Chapter 3.1 --- First Chern classes --- p.11 / Chapter 3.2 --- Semicharacters on line bundles --- p.12 / Chapter 3.3 --- Theorem of the Square --- p.14 / Chapter 4 --- Principally polarized abelian varieties --- p.16 / Chapter 4.1 --- Riemann Relations --- p.17 / Chapter 4.2 --- Characteristics of line bundles --- p.20 / Chapter 4.3 --- Theta Functions --- p.21 / Chapter 4.4 --- The Ox(l) bundle --- p.22 / Chapter 4.5 --- Metric on Ox(l) --- p.23 / Chapter 4.6 --- Abelian Varieties and Elliptic Curves --- p.24 / Chapter 5 --- Isogeny of Abelian Varieties --- p.26 / Chapter 5.1 --- Symmetric Line Bundles --- p.27 / Chapter 5.2 --- Theta Relations --- p.28 / Chapter 5.3 --- Theta Divisors --- p.30 / Chapter 6 --- Jacobians --- p.32 / Chapter 6.1 --- Jacobian as an abelian variety --- p.33 / Chapter 6.2 --- Abel-Jacobi Theorem --- p.36 / Chapter 6.3 --- Torelli´ةs theorem --- p.42 / Chapter 7 --- The Heisenberg Group --- p.43 / Chapter 8 --- Balanced Embedding into the Projective Space --- p.50

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