The key objective of this yearlong project was to learn serveral concepts in commuta- tive algebra and algebraic geometry. We started with learning concepts in commuta- tive algebra, which included primary decomposition, ...

Many topological spaces exist as the total spaces of real vector bundles over some base spaces. Topological properties like Hausdorffness, connectedness, the first axiom of countability, path connectedness, local connectedness ...

This thesis is divided into two parts, the first part is devoted to learning basic algebraic geometry and the second part is devoted to learning Cohomology and applying it to the settings of algebraic geometry.

This thesis discusses multihomogeneous spaces and their relation with T-varieties and toric varieties. Firstly, we study multihomogeneous spaces corresponding to $\mathbb{Z}^n$-graded algebras over an algebraically closed ...