Mathematics 797MD - ST-ModuliSpc&InvariantThy
Spring
2017
01
3.00
Evgueni Tevelev
M W F 9:05AM 9:55AM
UMass Amherst
20620
A moduli space appears each time we want to parametrize all geometric objects of some sort. "Geometry" in our course will mean mostly, but not exclusively, complex algebraic geometry. For example, elliptic curves are classified by the so-called J-invariant and the moduli space of elliptic curves is a line (with coordinate J). The Jacobian of a Riemann surface is another example of a moduli space: it classifies line bundles on a Riemann surface.
Introducing parameters for geometric objects (or, equivalently, local or global coordinates on the moduli space) is an art, or dark magic, which can be done in different ways: functorial approach (fine and coarse moduli spaces), geometric invariant theory, period domains, etc. Our approach will be based on examples: we will introduce many beautiful moduli spaces and develop whatever tools are convenient for their study.
Introducing parameters for geometric objects (or, equivalently, local or global coordinates on the moduli space) is an art, or dark magic, which can be done in different ways: functorial approach (fine and coarse moduli spaces), geometric invariant theory, period domains, etc. Our approach will be based on examples: we will introduce many beautiful moduli spaces and develop whatever tools are convenient for their study.
Open to Graduate students only. MATH 612 Note: An introductory course in Algebraic Geometry (such as MATH 797W: ST-Algebraic Geometry) is also a pre-requisite for this course.