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Abstract
This course is an Introduction to Algebraic Geometry (algebraic varieties and schemes).
Objective
Learning Algebraic Geometry.
Content
Affine Varieties The Zariski Topology The Sheaf of Regular Functions Morphisms Varieties Projective Varieties I: Topology Projective Varieties II: Ringed Spaces Grassmannians Birational Maps and Blowing Up Smooth Varieties The 27 Lines on a Smooth Cubic Surface Schemes Sheaves of Modules Quasi-coherent Sheaves Differentials Cohomology of Sheaves
Resources
Literature
Primary Reference: * Andreas Gathmann: Algebraic Geometry, https://agag-gathmann.math.rptu.de/class/alggeom-2021/alggeom-2021.pdf Secondary References: * Robin Hartshorne: Algebraic Geometry, Graduate Texts in Mathematics, Springer. * Miles Reid: Undergraduate Algebraic Geometry, Cambridge University Press. * Ravi Vakil: Foundations of Algebraic Geometry, http://math.stanford.edu/~vakil/216blog/ * David Eisenbud, Joe Harris: The Geometry of Schemes, Graduate Texts in Mathematics, Springer. * John Ottem, Geir Ellingsrud: Introduction to algebraic varieties, https://www.uio.no/studier/emner/matnat/math/MAT4210/data/mastermat4210.pdf * James Milne: Algebraic Geometry, http://www.jmilne.org/math/CourseNotes/AG.pdf * Qing Liu: Algebraic Geometry and Arithmetic Curves, Oxford Science Publications. * Ulrich Görtz and Torsten Wedhorn: Algebraic Geometry I, Advanced Lectures in Mathematics, Springer. * Igor Shafarevich: Basic Algebraic geometry 1 & 2, Springer-Verlag.