Lecture

Projective Varieties: An Algebraic Study

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In course

MATH-328: Algebraic geometry I - Curves

Algebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory. ...

Description

This lecture covers the study of projective varieties, which are the algebraic analogues of compact manifolds. The instructor explains the concept of irreducible sets in projective varieties and their relation to compact manifolds. The lecture delves into the algebraic level, discussing equations and lines in projective spaces. The instructor demonstrates how projective varieties are easier to study compared to compact manifolds. The lecture concludes with a discussion on closure properties and symmetric aspects of projective varieties.

Instructor

Dimitri Stelio Wyss

I did my PhD under the supervision of Tamas Hausel at EPFL and the Institue of Science and Technology Austria . From 2017-2019 I was a postdoctoral researcher at the Sorbonne University Paris 6 with François Loeser. Since September 2019 I hold the chair of arithmetic geometry at EPFL as a tenure track assistant professor. For more information see my CV.I work in algebraic and arithmetic geometry. My research uses ideas from p-adic and motivic integration to study the interplay between geometric and arithmet

Official source

Ontological neighbourhood

Mathematics

Geometry: Algebraic geometry

Related concepts (32)

Algebraic variety

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition. Conventions regarding the definition of an algebraic variety differ slightly.

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