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In 2002, an introductory workshop was held at the Mathematical
Sciences Research Institute in Berkeley to survey some of the many
directions of the commutative algebra field. Six principal speakers
each gave three lectures, accompanied by a help session, describing
the interaction of commutative algebra with other areas of
mathematics for a broad audience of graduate students and
researchers. This book is based on those lectures, together with
papers from contributing researchers. David Benson and Srikanth
Iyengar present an introduction to the uses and concepts of
commutative algebra in the cohomology of groups. Mark Haiman
considers the commutative algebra of n points in the plane. Ezra
Miller presents an introduction to the Hilbert scheme of points to
complement Professor Haiman's paper. Further contributors include
David Eisenbud and Jessica Sidman; Melvin Hochster; Graham
Leuschke; Rob Lazarsfeld and Manuel Blickle; Bernard Teissier; and
Ana Bravo.
In 2002, an introductory workshop was held at the Mathematical
Sciences Research Institute in Berkeley to survey some of the many
new directions of the commutative algebra field. Six principal
speakers each gave three lectures, accompanied by a help session,
describing the interaction of commutative algebra with other areas
of mathematics for a broad audience of graduate students and
researchers. This book is based on those lectures, together with
papers from contributing researchers. David Benson and Srikanth
Iyengar present an introduction to the uses and concepts of
commutative algebra in the cohomology of groups. Mark Haiman
considers the commutative algebra of n points in the plane. Ezra
Miller presents an introduction to the Hilbert scheme of points to
complement Professor Haiman's paper. David Eisenbud and Jessica
Sidman give an introduction to the geometry of syzygies, addressing
the basic question of relating the geometry of a projective variety
with an embedding into projective space to the minimal free
resolution of its coordinate ring over the polynomial ring of
ambient projective space. Melvin Hochster presents an introduction
to the theory of tight closure. to compute it. Rob Lazarsfeld and
Manuel Blickle discuss the theory of multiplier ideals and how they
can be used in commutative algebra. Bernard Teissier presents ideas
related to resolution of singularities, complemented by Ana Bravo's
paper on canonical subalgebra bases.
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