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As visiting professor at Seoul National University in 2008–2009, Hironaka mentored undergraduate student June Huh, a former high school drop-out and aspiring poet, encouraging his interest in pursuing math for graduate school. Huh won a Fields medal in 2022 for the linkages he found between algebraic geometry and combinatorics. [15]
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials ; the modern approach generalizes this in a few different aspects.
The first chapter, titled "Varieties", deals with the classical algebraic geometry of varieties over algebraically closed fields. This chapter uses many classical results in commutative algebra, including Hilbert's Nullstellensatz, with the books by Atiyah–Macdonald, Matsumura, and Zariski–Samuel as usual references. The second and the ...
In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0 , this was proved by Heisuke Hironaka in 1964; [ 1 ] while for varieties of dimension at least 4 over ...
The Éléments de géométrie algébrique (EGA; from French: "Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné) is a rigorous treatise on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the Institut des Hautes Études Scientifiques.
It contains many important results in plane and solid geometry, algebra (books II and V), and number theory (book VII, VIII, and IX). [52] More than any specific result in the publication, it seems that the major achievement of this publication is the promotion of an axiomatic approach as a means for proving results.
The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to cover "algebraic stacks and the algebraic geometry needed to define them".
He is best known for his work, starting with his thesis, on infinity categories and derived algebraic geometry. Derived algebraic geometry is a way of infusing homotopical methods into algebraic geometry, with two purposes: deeper insight into algebraic geometry (e.g. into intersection theory) and the use of methods of algebraic geometry in ...