Abstract:
In this paper we study Seidel's mirror map for abelian and Kummer surfaces. We find that mirror symmetry leads in a very natural way to the classical parametrization of Kummer surfaces in $\P^3$. Moreover, we describe a family of embeddings of a given abelian surface into noncommutative projective spaces.

Abstract:
The objective of this paper was to study the development of Piracanjuba (Brycon orbignyanus) in tanks under differents organic fertilizers. The experiment, entirely randomized, was accomplished in 16 tanks of 1000 liters, fertilized with manures of bovine (BOV), pigs (SUI), chickens (FRG) and others without fertilizer (SAO), using 15 fish/m3 with an initial average weight and length of 10,87+0,31 g e 9,78+0,07 cm. After 30 days, the experiment showed a uniform development of the fish and high survival rate in thestudied density. The treatments presented significant statistical differences (P<0,05) for weight gain and daily growth, except for the treatments BOV and SUI when compared to each other. The temperature and the dissolved oxygen were the abiotic factors that exerced a larger influence on the aquatic biota, affecting the development of the fish. Among the phytoplankton there was a larger presence of nanoplanktonic organisms favoring the development of the zooplankton, mainly the Clorophyta, with the Scenedesmus species, and the Cianophyta, with the Microcystis species, and among the zooplankton,the largest presence was of the rotifera from the species Brachionus and Keratella, followed by the copepods. The treatment fertilized with manure of chickens made possible a larger development of the plankton community, and better results of the development of the fish, demonstrating the importance of natural food in its diet. O objetivo deste trabalho foi estudar o desenvolvimento de juvenis de Piracanjuba (Brycon orbignyanus), em tanques com aduba es organicas. O experimento, inteiramente casualizado, foi realizado em 16 tanques de 1000 litros, adubados com estercos de bovinos (BOV), suínos (SUI), frangos de corte (FRG) e outros sem aduba o (SAO), utilizando 15 peixes/m3 com peso e comprimento médios iniciais de 10,87+0,31 g e 9,78+0,07 cm. Após 30 dias, o experimento mostrou um desenvolvimento uniforme dos peixes e alta taxa de sobrevivência na densidade estudada. Os tratamentos apresentaram diferen as estatisticamente significativas (p < 0,05) para ganho de peso e crescimento diário, com exce o dos tratamentos BOV e SUI quando comparados entre si. A temperatura e o oxigênio dissolvido foram os fatores abióticos que exerceram maior influência sobre a biota aquática, afetando o desenvolvimento dos peixes. Entre o fitoplancton houve maior abundancia de organismos nanoplanct nicos favorecendo o desenvolvimento do zooplancton, destacando-se as clorófitas, com o gênero Scenedesmus, e as cianofíceas, com o gênero Microcystis, e entre o zooplancton, a maio

Abstract:
We study coisotropic A-branes in the sigma model on a four-torus by explicitly constructing examples. We find that morphisms between coisotropic branes can be equated with a fundamental representation of the noncommutatively deformed algebra of functions on the intersection. The noncommutativity parameter is expressed in terms of the bundles on the branes. We conjecture these findings hold in general. To check mirror symmetry, we verify that the dimensions of morphism spaces are equal to the corresponding dimensions of morphisms between mirror objects.

Abstract:
We study generalized almost contact structures on odd-dimensional manifolds. We introduce a notion of integrability and show that the class of these structures is closed under symmetries of the Courant-Dorfman bracket, including T-duality. We define a notion of geometric type for generalized almost contact structures, and study its behavior under T-duality.

Abstract:
We study the canonical Poisson structure on the loop space of the super-double-twisted-torus and its quantization. As a consequence we obtain a rigorous construction of mirror symmetry as an intertwiner of the N=2 super-conformal structures on the super-symmetric sigma-models on the Kodaira-Thurston nilmanifold and a gerby torus of complex dimension 2. As an application we are able to identify global moduli of equivariant generalized complex structures on these target spaces with moduli of equivariant orthogonal complex structures on the doubled geometry.

Abstract:
We compute Seidel's mirror map for abelian varieties by constructing the homogeneous coordinate rings from the Fukaya category of the symplectic mirrors. The computations are feasible as only linear holomorphic disks contribute to the Fukaya composition in the case of the planar Lagrangians used. The map depends on a symplectomorphism $\rho$ representing the large complex structure monodromy. For the example of the two-torus, different families of elliptic curves are obtained by using different $\rho$ which are linear in the universal cover. In the case where $\rho$ is merely affine linear in the universal cover, the commutative elliptic curve mirror is embedded in noncommutative projective space. The case of Kummer surfaces is also considered.

Abstract:
We abstract Morimoto's construction of complex structures on product manifolds to pairs of certain generalized $F$-structures on manifolds that are not necessarily global products. As applications we characterize invariant generalized complex structures on product manifolds in which one factor is a Lie group and we generalize a theorem of Blair, Ludden and Yano on Hermitian bicontact manifolds.

Abstract:
We study the full sigma model with target the three-dimensional Heisenberg nilmanifold by means of a Hamiltonian formulation of double field theory. We show that the expected T -duality with the sigma model on a torus endowed with H-flux is a manifest symmetry of the theory. We compute correlation functions of scalar fields and show that they exhibit dilogarithmic singularities. We show how the reflection and pentagonal identities of the dilogarithm can be interpreted in terms of correlators with 4 and 5 insertions.

Abstract:
Berglund-H\"ubsch duality is an example of mirror symmetry between orbifold Landau-Ginzburg models. In this paper we study a D-module-theoretic variant of Borisov's proof of Berglund-H\"ubsch duality. In the $p$-adic case, the D-module approach makes it possible to endow the orbifold chiral rings with the action of a non-trivial Frobenius endomorphism. Our main result is that the Frobenius endomorphism commutes with Berglund-H\"ubsch duality up to an explicit diagonal operator.

Abstract:
Let $C$ be a nodal curve and $L$ be an invertible sheaf on $C$. Let $\alpha_{L}:C\dashrightarrow J_{C}$ be the degree-$1$ rational Abel map, which takes a smooth point $Q\in C$ to $\left[ m_{Q}\otimes L\right] $ in the Jacobian of $C$. In this work we extend $\alpha_{L}$ to a morphism $\overline{\alpha}_{L}:C\rightarrow\overline{J}_{E}^{P}$ taking values on Esteves' compactified Jacobian for any given polarization $E$. The maps $\overline{\alpha}_{L}$ are limits of Abel maps of smooth curves of the type $\alpha_{L}$.