Beauville surfaces, celebrated for their rich interplay between algebraic geometry and group theory, represent a striking class of complex algebraic surfaces constructed as quotients of products of ...

We prove the existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes 4 C P 2. These are the first examples of twistor spaces of algebraic ...

Commutative algebra and algebraic geometry form a deeply interwoven field that investigates the structure of polynomial rings, their ideals, and the geometric objects defined by these algebraic sets.

Syllabus: We will plan to cover approximately Chapter 2 and (time permitting) part of Chapter 3 of Hartshorne. For certain parts of the material, we will follow Vakil. Homework will consist of ...

Mathematics and physics share a close, reciprocal relationship. Mathematics offers the language and tools to describe physical phenomena, while physics drives the development of new mathematical ideas ...