Skip to main content

Hilbert schemes of points

  • Chapter
Combinatorial Commutative Algebra

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 227))

  • 6134 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  1. John Fogarty, Algebraic families on an algebraic surface, Amer. J. Math. 90 (1968), 511–521.

    MATH  MathSciNet  Google Scholar 

  2. Mark Haiman, Commutative algebra of N points in the plane, Lectures in Contemporary Commutative Algebra (L. Avramov, M. Green, C. Huneke, K. Smith, and B. Sturmfels, eds.), Mathematical Sciences Research Institute Publications, Cambridge University Press, Cambridge, 2004.

    Google Scholar 

  3. Mark Haiman, t, q-Catalan numbers and the Hilbert scheme, Discrete Math. 193 (1998), no. 1–3, 201–224.

    MATH  MathSciNet  Google Scholar 

  4. Hiraku Nakajima, Lectures on Hilbert schemes of points on surfaces, University Lecture Series Vol. 18, American Mathematical Society, Providence, RI, 1999.

    Google Scholar 

  5. L. Göttsche, Hilbert schemes of points on surfaces, Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), Higher Education Press, Beijing, 2002, pp. 483–494.

    Google Scholar 

  6. Anthony Iarrobino, Reducibility of the families of 0-dimensional schemes on a variety, Invent. Math. 15 (1972), 72–77.

    Article  MATH  MathSciNet  Google Scholar 

  7. Bernd Sturmfels, Four counterexamples in combinatorial algebraic geometry, J. Algebra 230 (2000), no. 1, 282–294.

    Article  MATH  MathSciNet  Google Scholar 

  8. Torsten Ekedahl and Roy Skjelnes, Recovering the good component of the Hilbert scheme, preprint, 2004. arXiv:math.AG/0405073

    Google Scholar 

  9. Mark Haiman, Hilbert schemes, polygraphs and the Macdonald positivity conjecture, J. Amer. Math. Soc. 14 (2001), no. 4, 941–1006. (electronic).

    Article  MATH  MathSciNet  Google Scholar 

  10. Mark Haiman, Vanishing theorems and character formulas for the Hilbert scheme of points in the plane, Invent. Math. 149 (2002), no. 2, 371–407.

    Article  MATH  MathSciNet  Google Scholar 

  11. Hermann Weyl, The classical groups, Their invariants and representations, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997 (reprint of the 1946 second edition).

    Google Scholar 

  12. Joël Briançon, Description de HilbnC{x, y}, Invent. Math. 41 (1977), no. 1, 45–89.

    MATH  MathSciNet  Google Scholar 

  13. Mark Haiman, Combinatorics, symmetric functions, and Hilbert schemes, Current developments in mathematics, 2002, International Press, Somerville, MA, 2003, pp. 39–111.

    Google Scholar 

  14. Mark Haiman and Bernd Sturmfels, Multigraded Hilbert schemes, J. Alg. Geom. 13 (2004), no. 4, 725–769.

    MathSciNet  Google Scholar 

  15. Isabella Novik, Alexander Postnikov, and Bernd Sturmfels, Syzygies of oriented matroids, Duke Math. J. 111 (2002), no. 2, 287–317.

    MathSciNet  Google Scholar 

  16. Diane Maclagan and Gregory G. Smith, Uniform bounds on multigraded regularity, J. Alg. Geom., to appear, 2004. arXiv:math.AG/0305215

    Google Scholar 

  17. Diane Maclagan and Gregory G. Smith, Multigraded Castelnuovo-Mumford regularity, J. Reine Angew. Math. 571 (2004), 179–212.

    MathSciNet  Google Scholar 

  18. David Eisenbud and Joe Harris, The geometry of schemes, Graduate Texts in Mathematics Vol. 197, Springer-Verlag, New York, 2000.

    Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

(2005). Hilbert schemes of points. In: Combinatorial Commutative Algebra. Graduate Texts in Mathematics, vol 227. Springer, New York, NY. https://doi.org/10.1007/0-387-27103-1_18

Download citation

Publish with us

Policies and ethics