Stable bundles on hypercomplex surfaces

TL;DR: In this article, the notion of positivity in fiber bundles and positive toric bundles was introduced and shown to be a generalization of the Borel-Remmert-Tits theorem.

TL;DR: In this article, the authors developed a spin-rotation procedure to transform a stable holomorphic structure on a vector bundle over a complex torus of dimension 4 into a new stable structure over a different torus.

TL;DR: In this article, the authors make a survey of the twistor theory for hypercomplex, generalized almost quaternionic manifold equipped with an appropriate connection admit a twistor space which comes naturally equipped with a tautological almost generalized complex structure.

Abstract: The objective of IbM programs about Entrepreneurs Empowerment of Endog Lewo and Comring chips in Sukajaya villages is to empower the entrepreneurs of micro UMKM who produce chips traditionally made from cassava and tapioca flour in Sukajaya villages, Malangbong Garut. Generally, the entrepreneur problems is production process and business management that is still conventional. The specific target that wants to be achieved from this program is the entrepreneurs are able to simply expand the product and apply business management such as separating personal and business finance, business recording and accounting, applying product marketing strategy and improving entrepreneurship motivation. The method used in order to achieve program objectives is trough individual approaches to the entrepreneurs and employers who involved in production activities. The approaches are: (1) counselling approach in order to improve entrepreneur knowledge, (2) training approach in order to improve entrepreneur skill in managing business, and (3) awareness approach in order to improve entrepreneurship act and motivation. In general, the planning of IbM activity program is surveying the similar business in Sukajaya village, then two entrepreneur partner who are suitable to be targeted by the IbM program are chosen. It is discussed the weakness and obstacles from production aspect and business management with the program partners. Furthermore, several counselling programs, training, product improvement demonstrations and discussions will be conducted in order to increasing the knowledge, skills and attitudes of entrepreneurs’ partner in managing their business. The result of this counselling and training activity has succeeded, although it has not maximally achieved. Some of the businessman has already practiced simple management in their business accounting and tried to access business capital to the bank. The sustainability of the IbM program is expected to continue and to be seen from the results of the impact evaluation and final evaluation that will be carried out on business actors who are quite successful with small business actors or newbies.

TL;DR: Generalized complex geometry encompasses complex and symplectic ge- ometry as its extremal special cases as mentioned in this paper, including generalized complex branes, which interpolate be- tween at bundles on Lagrangian submanifolds and holomorphic bundles on complex sub-mansifolds, and the basic properties of this geometry, including its enhanced symmetry group, elliptic deforma- tion theory, relation to Poisson geometry, and local structure theory.

TL;DR: A geometrical structure on even-dimensional manifolds is defined in this paper, which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold.

TL;DR: In this paper, the twisted chiral multiplet is used to formulate supersymmetric nonlinear σ-models with N = 2,4 extended supersymmetry, which fall outside the classification given by Alvarez-Gaume and Freedman.

TL;DR: A geometrical structure on even-dimensional manifolds is defined in this paper, which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold.