Components of Hilbert Schemes
This web page contains material for the workshop
Components of Hilbert Schemes.
Contributions from the workshop participants are available in
dvi,
postscript or
pdf.
Suggested reading
We wish to highlight the following papers which give an introduction to the
three problems that will be the focus of the workshop.
- The Hilbert scheme Hilbd(An) of d points in
affine n-space: Anthony Iarrobino describes the state of the art in
1985 in Hilbert scheme of points: overview of last ten years in
Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 297-320,
Proc. Sympos. Pure Math., 46, Part 2, Amer. Math. Soc., Providence, RI, 1987 (Mathscinet).
Dustin A. Cartwright, Daniel Erman, Mauricio Velasco, and Bianca Viray provide
some updates in Hilbert schemes of 8 points,
Algebra Number Theory, 3 (2009), no. 7, 763-795 (arXiv, Mathscinet).
- The locally Cohen-Macaulay locus in the Hilbert scheme of curves of
degree d and genus g in P3:
Robin Hartshorne provides an overview in Questions of connectedness of the
Hilbert scheme of curves in P3, in Algebra, arithmetic and geometry
with applications (West Lafayette, IN, 2000), 487-495, Springer, Berlin,
2004 (arXiv, Mathscinet).
- Components of multigraded Hilbert schemes: Mark Haiman and
Bernd Sturmfels introduced these parameter spaces in Multigraded
Hilbert schemes, Journal of Algebraic Geometry, 13 (2004) no. 4,
725-769 (arXiv, Mathscinet).
A lengthy, though not comprehensive, bibliography on Hilbert schemes is
available.
------------
A list of registered participants is available.
Questions or comments to workshops@aimath.org