(a) Recent refereed papers

  1. Li, Ping, Patil, D.P. and Roberts, L.G. Bases and Ideal Generators for Projective Monomial Curves, to appear in Communications in Algebra, pdf
  2. Omidali, M. and Roberts, L.G. On the Regularity of Certain Projective Monomial Curves, to appear in the Illinois Journal of Mathematics
  3. Cooper, Susan and Roberts, L.G. Algebraic Interpretation of a Theorem of Clements and Lindstrom, Journal of Commutative Algebra, 1(3)(2009)361-380. (an earlier version of this is Seminar Notes 3 below).
  4. Reid, Les, and Roberts,L.G. Maximal and Cohen-Macaulay Projective Monomial Curves, Journal of Algebra 307 (2007)409-423 (see below for a slightly expanded version)
  5. Reid, Les, and Roberts,L.G. Non-Cohen-Macaulay Projective Monomial Curves, Journal of Algebra 291(2005)171-186 ps
  6. De Quehen,V. and Roberts,L.G., Non-Cohen-Macaulay Projective Monomial Curves with Positive h-Vector, Canadian Mathematical Bulletin, 48(2)(2005)203-210 dvi
  7. Reid,Les and Roberts,L.G. and Vitulli, M., Some Results on Normal Homogeneous Ideals, dvi Communications in Algebra (31)(2003)4485-4506
  8. Patil, D.P. and Roberts, L.G. Hilbert functions of monomial curves, dvi Journal of Pure and Applied Algebra 183(2003)275-292
  9. Reid, Les. and Roberts, L.G., Monomial Subrings in Arbitrary Dimension, ps source (latex2e and auxiliary files. Uses pstricks and xypic) Journal of Algebra 236,703-730 (2001)
  10. Roberts, L.G. and Singh B., Weak Subintegrality and Invertible Modules in Graded Rings, dvi Journal of Algebra 237, 657-672(2001)
  11. Roberts, L.G., Integral dependence and weak subintegrality, dvi Contemporary Mathematics Volume 266, 2000, 23-28.
  12. Reid, Les. and Roberts, L.G., Monomial Subrings and Systems of Subintegrality, JPAA, 151 (2000) 287-299 dvi ps
  13. Geller,Sue, Maloo, A., Patil, D.P. and Roberts, L.G., Kahler differentials of affine monomial curves. dvi ps Beitrage zur Algebra und Geometrie 41 (2000) 67-84
  14. Roberts, L.G. Kahler Differentials of Certain Cusps, Algebraic K-Theory (V.P.Snaith, Editor) Fields Institute Communications, American Mathematical Society, 1997, 279-284.
  15. Reid, Les, Roberts, L.G., Singh, B. On weak subintegrality, Journal of Pure and Applied Algebra, 114, 1996, 93-109.
  16. Roberts, L.G., Reid, Les, A new criterion for weak subintegrality, Communications in Algebra, 24 (10), 1996, 3335-3342.
  17. Roberts, L.G. A remark on the Hochschild homology of the co-ordinate axes, Communications in Algebra, 24 (3), 1996, 949-953.
  18. Roberts, L.G. Certain projective curves with unusual Hilbert function, Journal of Pure and Applied Algebra, 104, 1995, 303-311.
  19. Reid, Les, Roberts, L.G., Singh, B. The structure of generic subintegrality, Proceedings of the Indian Academy of Sciences (Math. Sci.) 105, 1995, 1-22.
  20. Roberts, L.G., Singh, B. Invertible Modules and Generic Subintegrality, Journal of Pure and Applied Algebra, 95, 1994, 331-351.
  21. Roberts, L.G. Remarks on graded integral domains of dimension one over a finite field, Zero Dimensional Schemes (F. Orecchia and L. Chiantini, editors) de Gruyter, 1994, 307-315.
  22. Roberts, L.G., Reid, Les and Singh, B. Finiteness of subintegrality, Algebraic K-Theory and Algebraic Topology (P. Goerss and J. Jardine, editors) Kluwer Academic Publishers, 1993, 223-227.
  23. Roberts, L.G., and Singh B. Subintegrality, invertible modules, and the Picard Group, Compositio Mathematica 85, 1993, 249-279.
  24. Roberts, L.G., Reid, Les, Intersection points of seminormal configurations of lines, Contemporary Mathematics, Vol. 126, 1992, 151-162.
  25. Roberts, L.G., Reid, Les and Roitman, M. On Complete Intersections and their Hilbert Functions, Canadian Mathematical Bulletin 34, 1991, 525-535.
  26. Roberts, L.G., with an appendix by C. Weibel, Kahler Differentials and HC1 of certain graded K-algebras, Algebraic K-Theory: Connections with Geometry and Topology (ed. by J. F. Jardine and V. Snaith), pp. 389-424. Kluwer 1989.
  27. Roberts, L.G., On the lifting problem over an algebraically closed field, Mathematical Reports of the Academy of Science, Volume XI, 1989, 35-38.
  28. Roberts, L.G., Roitman, M., On Hilbert functions of reduced and of integral algebras, Journal of Pure and Applied Algebra 56, 1989, 85-104.
  29. Roberts, L.G., The Hilbert function of some reducible varieties, Communications in Algebra 15, 1987, 2371-2378.
  30. Roberts, L.G., The Seminormalization of a Union of Lines, Mathematical Reports of the Academy of Science, Volume IX, 1987, 37-41.
  31. Roberts, L., The Ideal Generation Conjecture for 28 Points in P3, Canadian Journal of Mathematics, 38, 1986, 1228-1238, Correction 39, 1987, 512.
  32. Roberts, L., Singh, B., Seminormality and Cohomology of Projective Varieties, Journal of Algebra, 103, 1986, 500-519.
  33. Roberts, L.G., with B.H. Dayton, The Hilbert polynomial of a union of lines, Contemporary Mathematics Vol. 55, 421-435, 1986.
  34. Geramita, A., Gregory, D., Roberts, L., Monomial Ideals and Points in Projective Space, Journal of Pure and Applied Algebra, 40, 33-62, 1986.

(b) Other publications (technical reports, book chapters, etc.)

  1. Roberts,L.G., The Ring of Witt Vectors. The Curves Seminar at Queen's XI. A.V.Geramita (Editor) Queen's Papers in Pure and Applied Mathematics, Vol.105, 2-26. dvi ps
  2. Roberts, L.G., A question "How many zero dimensional 0-sequences of degree d are there?" in Zero Dimensional Schemes (F. Orecchia and L. Chiantini, editors) de Gruyter 1994.
  3. Roberts, L.G., Lines in singular cubics. The Curves Seminar at Queen's, Volume 4. Queen's Papers in Pure and Applied Mathematics, Vol. 76. Queen's University, Kingston, Ontario 1986.

Recent papers to download

  1. Reid, Les, and Roberts,L.G. Maximal and Cohen-Macaulay Projective Monomial Curves, To Appear in the Journal of Algebra ps
    (This preprint contains two long technical proofs that will be omitted from the published version).

Slides of talks

  1. Roberts, L.G., Ideal Class Groups of Subintegral Extensions, ps Route 81 conference, Kingston, Oct. 24, 1998.
  2. Roberts, L.G., Monomial Subrings and Systems of Subintegrality, ps source Route 81 conference, Syracuse, Oct. 23, 1999.
  3. Roberts, L.G., The conductor of a submonoid of Zn, dvi source ps(fig 1) ps(fig2) Talk at Toronto AMS meeting, Special Session on Commutative Algebra and Algebraic Geometry Oct.23,00. The figures go after slide 5.
  4. Roberts, L.G., Projective Monomial Curves, Acireale, June 2002, ps
  5. Roberts,L.G. (joint with Les Reid), Non Cohen-Macaulay Projective Monomial Curves, CMS Montreal,December 04, ps
  6. Roberts,L.G. (joint with Les Reid and Mehdi Omidali), Projective Monomial Curves, AMS Vancouver, October 08, ps(talk) ps(table 1) ps(table 2). Table 1 goes after slide 5, table 2 at the end.
  7. Roberts,L.G. (joint with Ping Li), Ideal Generators of Projective Monomial Curves in P3, Queen's Algebraic Geometry Seminar, March 23, 2015 pdf

Lecture notes on integral closure.

  lecture notes(ps)|source code(zip)
These notes are intended for beginning graduate students, and form part of the background for my current research with Les Reid. Notes taken by Susan Cooper. The source code is offered also, in case anyone is interested. This is in latex2e, with xypic and pstricks. For convenience in editing, the pictures are in separate files. Corrections from Marie Vitulli added Oct.5, 00.

Seminar notes and other exposition

  1. Concluding Lectures of reading course on Cohen-Macaulay Rings (March 02) ps
  2. Type Vectors and Hilbert Functions (Feb.26, 02) ps
  3. Algebraic Interpretation of a theorem of Clements and Lindstrom (with Susan Cooper) Dec.12,03 dvi

If you are in an organization which subscribes to the AMS' MathSciNet, reviews of some of these papers are available.