Daniel Daigle
Professeur émérite / Emeritus Professor
 		Département de mathématiques et statistiques
Faculté des sciences
Université d'Ottawa
 		Department of mathematics and statistics
Faculty of science
University of Ottawa


Research
General area

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


Research areas
  • Geometry of affine spaces
  • Classification of affine varieties
  • Ga-actions on affine spaces and affine varieties
  • Locally nilpotent derivations on commutative rings
  • Hilbert 14th Problem
  • Algebraic surfaces
Publications
D. Daigle, Locally nilpotent derivations and the structure of rings. To appear in J. of Pure and Applied Algebra.   arXiv:1806.10742 [math.AG]
D. Daigle, Rings with trivial FML-invariant.  To appear in Transformation Groups.  
arXiv:1806.10739 [math.AG]
D. Daigle, Locally nilpotent sets of derivations.  To appear in Polynomial rings and Affine Algebraic Geometry, Tokyo, Japan, February 2018.  Springer Proceedings Math. Stat. 

arXiv:1901.04105 [math.AC]

Y. Y. Bao and D. Daigle, Small embeddings of integral domains, to appear in Kyoto J. Math.
pdf
D. Daigle, G. Freudenburg and L. Moser-Jauslin, Locally Nilpotent Derivations of Rings Graded by an Abelian Group.  Algebraic varieties and automorphism groups, Adv. Stud. Pure Math. 75 (2017), 29-48, Math. Soc. Japan, Tokyo.
 pdf
Pi. Cassou-Noguès and D. Daigle, Rational polynomials of simple type: a combinatorial proof.  Algebraic varieties and automorphism groups, Adv. Stud. Pure Math. 75 (2017), 7–28, Math. Soc. Japan, Tokyo.
 pdf
Pi. Cassou-Noguès and D. Daigle, Sets of polynomial rings in two variables and factorizations of polynomial morphisms.  J. Algebra 461 (2016), 129–163.
 pdf
Pi. Cassou-Noguès and D. Daigle, Field generators in two variables and birational endomorphisms of A2, J. Algebra Appl. 14 (2015), no. 9, 1540005, 35 pp.
 pdf
D. Daigle, Generally rational polynomials in two variables, Osaka J. Math. 52 (2015), 139--159.
 pdf
Pi. Cassou-Noguès and D. Daigle, Very good and very bad field generators, Kyoto J. Math., 55 (2015), 187-218.
 pdf
Pi. Cassou-Noguès and D. Daigle, Compositions of birational endomorphisms of the affine plane, Pacific J. Math. 272 (2014), 353--394.
 pdf
D. Daigle and A. Melle-Hernández, Linear systems associated to unicuspidal rational plane curves, Osaka J. Math. 51 (2014), 481–511.
 pdf
D. Daigle and A. Melle-Hernández, Linear systems of rational curves on rational surfaces, Mosc. Math. J. 12 (2012), 261–268.
pdf
D. Daigle and R. Kolhatkar, Complete intersection surfaces with trivial Makar-Limanov invariant, J. of Algebra, 350 (2012), 1-35. pdf
D. Daigle, Polynomials f(X,Y,Z) of low LND-degree, CRM Proceedings & Lecture Notes 54 (2011), 21-34.
 pdf
D. Daigle, Tame and wild degree functions, Osaka J. of Math. 49 (2012), 53-80.
 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], Canad. Math. Bull. 52 (2009), 535-543.
 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)
M. Chitayat and D. Daigle, On the rigidity of certain Pham-Brieskorn rings.
 arXiv:1907.13259 [math.AC]
Pi. Cassou-Noguès and D. Daigle, Structure of the Newton tree at infinity of a polynomial in two variables. arXiv:1809.02462v2 [math.AG]


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