Daniel Daigle
Professeur Titulaire / Professor 		Faculté des sciences
Faculty of Science

Cours / Courses
  MAT1341A
 Introduction to linear algebra
 Fall 2009
  MAT2362
Foundations of mathematics
(Logic and set theory)
 Fall 2009
Recherche / Research
General area

Algebraic geometry, commutative algebra.
Affine geometry (2000 Subject Classification: 14R)


Research areas
  • Geometry of affine spaces
  • Additive actions on affine spaces
  • Locally nilpotent derivations
  • Hilbert 14th Problem
  • Algebraic surfaces
Publications
 D. Daigle, Triangular derivations of k[X,Y,Z], to appear in JPAA.
 pdf
 S.M. Bhatwadekar and D. Daigle, On finite generation of kernels of locally nilpotent R-derivations of R[X,Y,Z], to appear in J. of Algebra.
 pdf
 D. Daigle and G. Freudenburg, Families of affine fibrations, to appear in Progress in Mathematics.
 pdf
D. Daigle, Affine surfaces with trivial Makar-Limanov invariant, J. Algebra 319 (2008), 3100-3111.
 pdf
 ps
D. Daigle, On polynomials in three variables annihilated by two locally nilpotent derivations, J. of Algebra 310 (2007), 303-324. dvi ps
 D. Daigle, Classification of homogeneous locally nilpotent derivations of  k[X,Y,Z].  Part I: Positive gradings of positive type, Transf. Groups 12 (2007), 33-47.
 pdf
 ps
D. Daigle, Classification of linear weighted graphs up to blowing-up and blowing-down, Canad. J. of Math. 60 (2008), 64-87.
 pdf ps
D. Daigle and P. Russell, On log Q-homology planes and weighted projective planes, Canadian J. Math. 56 (2004),  1145-1189.
 dvi ps
D. Daigle and S. Kaliman, A note on locally nilpotent derivations and variables of k[X,Y,Z],  to appear in Canad. Math. Bull.
 dvi ps
D. Daigle,  Locally nilpotent derivations and Danielewski surfaces, Osaka J. Math. 41, (2004), 37-80.
 dvi ps
D. Daigle,  On locally nilpotent derivations of  k[X,Y,Z] / (XY-P(Z)),  JPAA 181 (2003), 181-208. dvi ps
D. Daigle and G. Freudenburg, Triangular derivations of k[X1,X2,X3,X4], J. of Algebra 241 (2001), 328-339.  dvi ps
D. Daigle and P. Russell, Affine rulings of normal rational surfaces, Osaka J. Math. 38 (2001), pp. 37-100.  dvi ps
D. Daigle and P. Russell, On weighted projective planes and their affine rulings, Osaka J. Math. 38 (2001), 101-150.  dvi ps
D. Daigle, Affine rulings of weighted projective planes, Annales Polonici Mathematici LXXVI.1-2 (2001), 47-66. 
dvi
ps
D. Daigle, On kernels of homogeneous locally nilpotent derivations of k[X,Y,Z], Osaka J. Math. 37 (2000), 689-699. 
dvi
ps
D. Daigle and G. Freudenburg,  A note on triangular derivations of k[X1,X2,X3,X4], Proceedings of the AMS 129 (2000), 657-662. 
dvi
ps
D. Daigle and G. Freudenburg, A counterexample to Hilbert's Fourteenth Problem in dimension five, J. of Algebra 221 (1999), 528-535. 
dvi
ps
D. Daigle, Homogeneous locally nilpotent derivations of k[X,Y,Z], J. Pure Appl. Algebra 128 (1998), 109-132. 
dvi
ps
D. Daigle, A necessary and sufficient condition for triangulability of derivations of k[X,Y,Z], J. Pure Appl. Algebra 113 (1996), 297-305.   
ps
D. Daigle and G. Freudenburg, Locally nilpotent derivations over a UFD and an application to rank two locally nilpotent derivations of k[X1,...,Xn],  J. of Algebra 204 (1998), 353-371.   pdf
D. Daigle, On some properties of locally nilpotent derivations, J. Pure Appl. Algebra 114 (1997), 221-230.
D. Daigle, On pencils of polynomial curves, J. Pure Appl. Algebra 111 (1996), 51-57.
D. Daigle, On purely inseparable extensions k[X,Y]/k[X^p,Y^p] and their generators, Proc. Amer. Math. Soc. 124 (1996), 1337-1345.
D. Daigle, Purely inseparable extensions of k[X,Y], Proc. Amer.  Math. Soc. 121 (1994), 1-12.
D. Daigle, Plane Frobenius sandwiches of degree p, Proc. Amer. Math.  Soc. 117 (1993), 885-889.
D. Daigle, A property of polynomial curves over a field of positive characteristic, Proc. Amer. Math. Soc. 109 (1990), 887-894.
D. Daigle, Relative Frobenius of plane singularities, Trans. Amer.  Math. Soc. 324 (1991), 777-791.
D. Daigle, Local trees in the theory of affine plane curves, J. Math. Kyoto Univ. 31 (1991), no. 3, 593-634.
D. Daigle, Birational endomorphisms of the affine plane, J. Math. Kyoto Univ. 31 (1991), no. 2, 329-358.
Other (submitted papers)
 D. Daigle and R. Kolhatkar, Complete intersection surfaces with trivial Makar-Limanov invariant.


Other (non refereed texts)
D. Daigle, Some problems and methods of affine algebraic geometry. 
Lecture notes for a short course given at the Universidad Complutense de Madrid, April 2008.
 pdf
D. Daigle, Hilbert's Fourteenth Problem and locally nilpotent derivations. 
This was written to prepare the survey talk with the same title, Oberwolfach, January 2007.
 pdf
 ps
D. Daigle, Classification of weighted graphs up to blowing-up and blowing-down, arXiv:math.AG/0305029, 2003. pdf
 ps
D. Daigle, Locally nilpotent derivations.  Lecture notes prepared for the "September School of algebraic geometry", Lukecin, Poland, September 2003.
 pdf
 ps


Contact
Département de Mathématiques et Statistiques
Université d'Ottawa

585 Rue King-Edward
Ottawa, Ontario, Canada, K1N 6N5
Department of Mathematics and Statistics
University of Ottawa

585 King-Edward
Ottawa (Ontario), Canada, K1N 6N5
Téléphone: (613) 562-5800 x 3521
Télécopieur: (613) 562-5776
Courriel: ddaigle@uottawa.ca

Telephone: (613) 562-5800 x 3521
Fax: (613) 562-5776
Email: ddaigle@uottawa.ca
Bureau: KED, piece 301-C
Office: KED, room 301-C