Daniel Daigle

Cours / Courses

MAT1748	Mathématiques discrètes pour l'informatique	hiver 2012
MAT2748	Mathématiques discrètes	hiver 2012

Research projects for students
If you consider the possibility of studying under my supervision, you can find some useful information here.

Research

General area

Algebraic geometry, commutative algebra.
Affine algebraic geometry (2010 Subject Classification: 14R)

Research areas

Geometry of affine spaces
Classification of affine varieties
G_a-actions on affine spaces and affine varieties
Locally nilpotent derivations on commutative rings
Hilbert 14th Problem
Algebraic surfaces

Publications

D. Daigle and A. Melle-Hernández, Linear systems of rational curves on rational surfaces, to appear in Moscow Math J.	pdf
D. Daigle and R. Kolhatkar, Complete intersection surfaces with trivial Makar-Limanov invariant, to appear in J. of Algebra. DOI:10.1016/j.jalgebra.2011.09.032	pdf
D. Daigle, Polynomials f(X,Y,Z) of low LND-degree, in "Affine Algebraic Geometry: The Russell Festschrift", CRM Proceedings & Lecture Notes 54 (2011).	pdf
D. Daigle, Tame and wild degree functions, Osaka J. of Math. 49 (2012).	pdf
D. Daigle, Triangular derivations of k[X,Y,Z], J. of Pure and Applied Algebra 214 (2010), 1173-1180.	pdf
S.M. Bhatwadekar and D. Daigle, On finite generation of kernels of locally nilpotent R-derivations of R[X,Y,Z], J. of Algebra 322 (2009), 2915-2926.	pdf
D. Daigle and G. Freudenburg, Families of affine fibrations, Progress in Mathematics 278 (2010), 35-43.	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)

Other (non refereed texts)

D. Daigle, Introduction to locally nilpotent derivations, Lecture notes, 2010.	pdf
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
D. Daigle, Classification of weighted graphs up to blowing-up and blowing-down, arXiv:math.AG/0305029, 2003.	pdf
D. Daigle, Locally nilpotent derivations. Lecture notes prepared for the "September School of algebraic geometry", Lukecin, Poland, September 2003.	pdf

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