algebraic geometry 25 Morphisms of varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of a morphism of varieties and compares algebraic varieties with other types of locally ringed spaces.
From playlist Algebraic geometry I: Varieties
algebraic geometry 23 Categories
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a quick review of category theory as background for the definition of morphisms of algebraic varieties.
From playlist Algebraic geometry I: Varieties
algebraic geometry 26 Affine algebraic sets and commutative rings
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between morphisms of affine algebraic sets and homomorphisms of commutative rings. As examples it describes some homomorphisms of commutative rings
From playlist Algebraic geometry I: Varieties
Weil conjectures 7: What is an etale morphism?
This talk explains what etale morphisms are in algebraic geometry. We first review etale morphisms in the usual topology of complex manifolds, where they are just local homeomorphism, and explain why this does not work in algebraic geometry. We give a provisional definition of etale morphi
From playlist Algebraic geometry: extra topics
Schemes 10: Morphisms of affine schemes
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We try to define morphisms of schemes. The obvious definition as morphisms of ringed spaces fails as we show in an example. Instead we have to use the more su
From playlist Algebraic geometry II: Schemes
algebraic geometry 29 Automorphisms of space
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It describes the automorphisms of affine and projective space, and gives a brief discussion of the Jacobian conjecture.
From playlist Algebraic geometry I: Varieties
Schemes 41: Morphisms to projective space
This lecture is part of an online course on algebraic geometry based on chapter II of "algebraic geometry" by Hartshorne. We discuss morphisms of a scheme to projective space, showing that they correspond to a line bundle with a set of sections generating it.
From playlist Algebraic geometry II: Schemes
Schemes 16: Morphisms of finite type
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We introduce three properties of morphisms: quasicompact, finite type, and locally of finite type, and give a few examples.
From playlist Algebraic geometry II: Schemes
algebraic geometry 17 Affine and projective varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between affine and projective varieties, with some examples such as a cubic curve and the twisted cubic.
From playlist Algebraic geometry I: Varieties
On the long-term dynamics of nonlinear dispersive evolution equations - Wilhelm Schlag
Analysis Seminar Topic: On the long-term dynamics of nonlinear dispersive evolution equations Speaker: Wilhelm Schlag Affiliation: University of Chicago Visiting Professor, School of Mathematics Date: Febuary 14, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Ariyan Javanpeykar: Arithmetic and algebraic hyperbolicity
Abstract: The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of “rational points”. For instance, it suggests a striking answer to the fundamental question “Why do some polynomial equations with integer coefficients have onl
From playlist Algebraic and Complex Geometry
BAG1.3. Toric Varieties 3 - Coordinate Rings and Morphisms
Basic Algebraic Geometry: We introduce the notions of coordinate rings and morphisms, and use properties of tori as examples.
From playlist Basic Algebraic Geometry
Stefan Kebekus The geometry of singularities in the Minimal Model Program and applications to singul
This talk surveys recent results on the singularities of the Minimal Model Program and discusses applications to the study of varieties with trivial canonical class. The first part of the talk discusses an infinitesimal version of the classical decomposition theorem for varieties with vani
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Schemes 21: Separated morphisms
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We define separated and quasi-separated schemes and morphisms, give a few examples, and show that if a scheme has a separated morphism to an affine scheme the
From playlist Algebraic geometry II: Schemes
algebraic geometry 31 Rational maps
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of rational functions and rational maps, and gives an example of a cubic curve that is not birational to the affine line.
From playlist Algebraic geometry I: Varieties