Algebraic varieties, defined as the solution sets of polynomial equations over a field, exhibit rich geometric structures that have spurred substantial developments.

Mathematical Problem Solved After More Than 50 Years: Chern Numbers Of Algebraic Varieties. ScienceDaily . Retrieved June 3, 2025 from www.sciencedaily.com / releases / 2009 / 06 / 090610124858.htm ...

Algebraic Variety: A fundamental geometric object defined as the set of solutions to systems of polynomial equations. Cohomology: A collection of mathematical methods used to study topological ...

Globally F-regular variety: A type of algebraic variety in positive characteristic that exhibits strong regularity properties under Frobenius splitting, leading to favourable geometric and ...

Unlikely Intersections: Rare and structurally significant intersections in algebraic varieties where additional arithmetic or geometric conditions are met unexpectedly.

Algebraic varieties over $\mathbb{Q}$ are among the fundamental objects in arithmetic geometry. We aim to study them by establishing and studying new cohomology theories. Here, one of our main ...

The study of algebraic geometry encompasses the investigation of geometric structures defined by polynomial equations, with particular attention given to their intrinsic and extrinsic properties.