You do not have access to this resource. This article is an introduction to algebraic geometry and some of its applications. Reminders of commutative algebra (groups, rings, ideals, ring fields of ...

Algebraic and differential geometry stand as two intertwined pillars of modern mathematics. Whereas algebraic geometry investigates the solution sets of polynomial equations using the refined language ...

ABSTRACT: The purpose of this short but difficult paper is to revisit the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT) in the light of a modern approach to nonlinear ...

ABSTRACT: The correct formulation and understanding of micro-images is one of the difficulties that occur to microstructures science today, which need to develop a new appropriate mathematics for ...

Algebraic geometry has long provided a deep framework for understanding the solutions of polynomial equations through geometric lenses. In recent years, tropical geometry – a relatively young field – ...

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Algebraic geometry is a classical subject with a modern face that studies geometric objects defined by polynomial equations in several variables. The course introduces the basic objects in algebraic ...