- Cohen-Macaulay Rings and Systems of Parameters
.ps .dvi
-
A short note showing that a ring of invariants is CM if and only if
it is a free module over a system of parameters.
-
Non-Modular Invariant Theory
.ps .dvi.
-
A longer note dealing with some of Brauer's theory of invariants over Dedekind
domains. This theory allows us to compare properties of representations in
different characterstics. The notes deal only with the non-modular case, and
are still in progress.
-
Mori's Marvelous Method of Producing Rational Curves
.ps
-
A short note (with awkward pictures) written as an introduction to Mori's bend
and break method, also emphasizing the fact that Grothendieck's vision of
Algebraic Geometry allows us to compare geometric phenomena in different
characteristics.
-
Counting Covers of an Elliptic Curve
.ps.
-
An outline of the
Dijkgraaf-Kaneko-Zagier argument that the generating functions
counting simply branched genus g covers of an elliptic curve are given by quasimodular forms
of weight 6g-6. There are also some tables
(.ps .dvi
.pdf) for the number of
covers, and an atrociously typeset list of some of the modular forms
(.ps .dvi
.pdf).
-
Inverse Systems and Regular Representations
.ps. .dvi.
-
A note written for the Kingston workshop on inverse systems and diagonal
invariants. If G is a finite group acting via
a pseudo-reflection representation on a vector space V, then this note
characterizes the sets of polynomials on V such that the vector space
generated by
all their partial derivatives is a sum of copies of the regular
representation of G.
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