A Concise Introduction to Algebraic Varieties is designed for a
one-term introductory course on algebraic varieties over an
algebraically closed field, and it provides a solid basis for a
course on schemes and cohomology or on specialized topics, such as
toric varieties and moduli spaces of curves. The book balances
generality and accessibility by presenting local and global
concepts, such as nonsingularity, normality, and completeness using
the language of atlases, an approach that is most commonly
associated with differential topology. The book concludes with a
discussion of the Riemann-Roch theorem, the Brill-Noether theorem,
and applications. The prerequisites for the book are a strong
undergraduate algebra course and a working familiarity with basic
point-set topology. A course in graduate algebra is helpful but not
required. The book includes appendices presenting useful background
in complex analytic topology and commutative algebra and provides
plentiful examples and exercises that help build intuition and
familiarity with algebraic varieties.
General
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