364 research outputs found
A new unicity theorem and Erdos' problem for polarized semi-abelian varieties
No full textIn 1988 Erdös asked if the prime divisors of x n - 1 for all n = 1,2, determine the given integer x; the problem was affirmatively answered by Corrales-Rodrigáñez and Schoof (J Number Theory 64:276-290, 1997) [but a solution could also be deduced from an earlier result of Schinzel (Bull Acad Polon Sci 8:307-309, 2007)] together with its elliptic version. Analogously, Yamanoi (Forum Math 16:749-788, 2004) proved that the support of the pulled-back divisor f *D of an ample divisor on an abelian variety A by an algebraically non-degenerate entire holomorphic curve f:C → A essentially determines the pair (A, D). By making use of the main theorem of Noguchi (Forum Math 20:469-503, 2008) we here deal with this problem for semi-abelian varieties; namely, given two polarized semi-abelian varieties (A 1, D 1), (A 2, D 2) and algebraically non-degenerate entire holomorphic curves f i: C → A i, i = 1, 2,we classify the cases when the inclusion holds. We shall remark in §5 that these methods yield an affirmative answer to a question of Lang formulated in 1966. Our answer is more general and more geometric than the original question. Finally, we interpret the main result of Corvaja and Zannier (Invent Math 149:431-451, 2002) to provide an arithmetic counterpart in the toric case. © 2011 Springer-Verlag
I remember playing Sunday sandlot baseball at Seabrook
No full textIn this "I remember" memoir, Rei Noguchi recalls playing baseball during the summer months at Seabrook. Some families provided the equipment for everyone to use. Players on one team would share their baseball gloves with the players on the other. Each team kept its own score, as well as designated an umpire. Rei found that it worked very well. Often, the adults would play against the kids, and Rei remembers the kids winning more games. The games were usually community events, and people would stop by to watch while doing errands around the town. The Seabrook Educational and Cultural Center has been soliciting current and past residents of Seabrook Farms for an "I remember" project. Residents are asked to create narratives regarding their experiences at Seabrook Farms. These memories help preserve the history and multi-cultural heritage of Seabrook Farms
Bibliographical Review on the Academic Achievements of Dr. Hideyo Noguchi
No full textA complete list o farticles by Dr. Hideyo Noguchi was compiled by the author. The articles are classified and discussed. The quantity and range of the articles were impressive. The author expresses his great respect for Dr. Hideyo Noguchi, who was an excellent scientist and dedicated researcher
Bibliographical Review on the Academic Achievements of Dr. Hideyo Noguchi
No full textA complete list o farticles by Dr. Hideyo Noguchi was compiled by the author. The articles are classified and discussed. The quantity and range of the articles were impressive. The author expresses his great respect for Dr. Hideyo Noguchi, who was an excellent scientist and dedicated researcher
Quasi-positive orbifold cotangent bundles: Pushing further an example by Junjiro Noguchi
No full textIn this work, we investigate the positivity of logarithmic and orbifold cotangent bundles along hyperplane arrangements in projective spaces. We show that a very interesting example given by Noguchi (as early as in 1986) can be pushed further to a very great extent. Key ingredients of our approach are the use of Fermat covers and the production of explicit global symmetric differentials. This allows us to obtain some new results in the vein of several classical results of the literature on hyperplane arrangements. These seem very natural using the modern point of view of augmented base loci, and working in Campana's orbifold category
Degeneracy of holomorphic curves into algebraic varieties
No full textAbstractApplying the Second Main Theorem of [J. Noguchi, J. Winkelmann, K. Yamanoi, The second main theorem for holomorphic curves into semi-Abelian varieties II, Forum Math., in press, e-print archive, math.CV/0405492], we deal with the algebraic degeneracy of entire holomorphic curves f:C→X from the complex plane C into a complex algebraic normal variety X of positive log Kodaira dimension that admits a finite proper morphism to a semi-Abelian variety. We will also discuss applications to the Kobayashi hyperbolicity problem
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