On equivariant Serre problem for principal bundles

Let $E_G$ be a $\Gamma$--equivariant algebraic principal $G$--bundle over a normal complex affine variety $X$ equipped with an action of $\Gamma$, where $G$ and $\Gamma$ are complex linear algebraic groups. Suppose $X$ is contractible as a topological $\Gamma$--space with a dense orbit, and $x_0 \in X$ is a $\Gamma$--fixed point. We show that if $\Gamma$ is reductive, then $E_G$ admits a $\Gamma$--equivariant isomorphism with the product principal $G$--bundle $X \times_{\rho} E_G(x_0)$, where $\rho\,:\, \Gamma \, \longrightarrow\, G$ is a homomorphism between algebraic groups. As a consequence, any torus equivariant principal $G$-bundle over an affine toric variety is equivariantly trivial. This leads to a classification of torus equivariant principal $G$-bundles over any complex toric variety.Comment: References added. To appear in the International Journal of Mathematic

Tannakian classification of equivariant principal bundles on toric varieties

Let $X$ be a complete toric variety equipped with the action of a torus $T$ and $G$ a reductive algebraic group, defined over an algebraically closed field $K$. We introduce the notion of a compatible $\Sigma$--filtered algebra associated to $X$, generalizing the notion of a compatible $\Sigma$--filtered vector space due to Klyachko, where $\Sigma$ denotes the fan of $X$. We combine Klyachko's classification of $T$--equivariant vector bundles on $X$ with Nori's Tannakian approach to principal $G$--bundles, to give an equivalence of categories between $T$--equivariant principal $G$--bundles on $X$ and certain compatible $\Sigma$--filtered algebras associated to $X$, when the characteristic of $K$ is $0$.Comment: 22 pages, revised version, to appear in Transform. Group

A classification of equivariant principal bundles over nonsingular toric varieties

We classify holomorphic as well as algebraic torus equivariant principal $G$-bundles over a nonsingular toric variety $X$, where $G$ is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric variety admits a trivialization in equivariant sense. We also obtain some splitting results.Comment: 14 page

Restriction theorems for Higgs principal bundles

AbstractWe prove analogues of Grauert–Mülich and Flennerʼs restriction theorems for semistable principal Higgs bundle over any smooth complex projective variety

DESIGN AND EXPERIMENTAL ANALYSIS OF FURNACE FOR THE PRODUCTION OF BAMBOO CHARCOAL

This paper presents the study of carbonization systems for the production of Bamboo Charcoal which is formed on dry distillation of raw bamboo. The paper mentions the drawbacks of the conventional practices of production of Bamboo Charcoal. Design of a new charcoal production unit is aimed at eliminating the identified drawbacks in the present methodology of production making the process of production faster and more efficient by minimizing heat loss during the production process. Designing is attempted with strong consideration for manufacture, operational cost and ease of operation of the furnace as the process finds application amongst rural people with little or no technical knowhow, making simplicity of design absolutely critical for implementation of the developed technology. Results of testing and experimentation presented in this paper describe the working prototype confirming qualitative and quantitative improvements in the bamboo charcoal being produced as compared to the conventional method of production

Pollution management with techno-economical evaluation for coke based and cokeless furnaces concerning melting and casting of brass and bell metal

India is a very important global player in the casting sector not only of cast iron but also of non-ferrous sector such as brass and bell metal. Melting furnaces of these are mainly coke based. There is also a growing awareness of pollution control levels in the country in recent times and this is a perceived as a threat to the existence of these small scale foundries including melting unit for casting for brass and bell metals scattered in various parts of the country. Attempt has been made to carry out research and development work on developing various modules eco-friendly furnaces concerning melting and of brass and bell metal casting/ product. This paper also discusses technoeconomical aspect of the mentioned coke based and coke less furnaces concerning brass and bell metal product