Daniel Daigle
Professeur Titulaire / Professor
Département de mathématiques et statistiques
Faculté des sciences

Université d'Ottawa
Department of mathematics and statistics
Faculty of science

University of Ottawa

Cours / Courses
MAT 1748   Mathématiques discrètes pour l'informatique       hiver 2017
MAT 2748   Mathématiques discrètes
  hiver 2017

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
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.
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D. Daigle, Generally rational polynomials in two variables, Osaka J. Math. 52 (2015), 139--159.
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Pi. Cassou-Noguès and D. Daigle, Very good and very bad field generators, Kyoto J. Math., 55 (2015), 187-218.
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Pi. Cassou-Noguès and D. Daigle, Compositions of birational endomorphisms of the affine plane, Pacific J. Math. 272 (2014), 353--394.
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D. Daigle and A. Melle-Hernández, Linear systems associated to unicuspidal rational plane curves, to appear in Osaka J. Math. 51 (2014), 481–511.
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D. Daigle and A. Melle-Hernández, Linear systems of rational curves on rational surfaces, Mosc. Math. J. 12 (2012), 261–268.
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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.
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D. Daigle, Tame and wild degree functions, Osaka J. of Math. 49 (2012), 53-80.
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D. Daigle, Triangular derivations of k[X,Y,Z], J. of Pure and Applied Algebra 214 (2010), 1173-1180.
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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.
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D. Daigle and G. Freudenburg, Families of affine fibrations, Progress in Mathematics 278 (2010), 35-43.
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D. Daigle, Affine surfaces with trivial Makar-Limanov invariant, J. Algebra 319 (2008), 3100-3111.
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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.
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D. Daigle, Classification of linear weighted graphs up to blowing-up and blowing-down, Canad. J. of Math. 60 (2008), 64-87.
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D. Daigle and P. Russell, On log Q-homology planes and weighted projective planes, Canadian J. Math. 56 (2004),  1145-1189.
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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.
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D. Daigle,  Locally nilpotent derivations and Danielewski surfaces, Osaka J. Math. 41, (2004), 37-80.
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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. 
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D. Daigle, On kernels of homogeneous locally nilpotent derivations of k[X,Y,Z], Osaka J. Math. 37 (2000), 689-699. 
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D. Daigle and G. Freudenburg,  A note on triangular derivations of k[X1,X2,X3,X4], Proceedings of the AMS 129 (2000), 657-662. 
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D. Daigle and G. Freudenburg, A counterexample to Hilbert's Fourteenth Problem in dimension five, J. of Algebra 221 (1999), 528-535. 
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D. Daigle, Homogeneous locally nilpotent derivations of k[X,Y,Z], J. Pure Appl. Algebra 128 (1998), 109-132. 
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D. Daigle, A necessary and sufficient condition for triangulability of derivations of k[X,Y,Z], J. Pure Appl. Algebra 113 (1996), 297-305.   
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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)
Pi. Cassou-Noguès and D. Daigle, Sets of polynomial rings in two variables and factorizations of polynomial morphisms.

Pi. Cassou-Noguès and D. Daigle, Simple rational polynomials: a combinatorial proof.

D. Daigle, G. Freudenburg and L. Moser-Jauslin, Locally Nilpotent Derivations of Rings Graded by an Abelian Group.



Other (non refereed texts)
D. Daigle, Introduction to locally nilpotent derivations, Lecture notes, 2010.
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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.
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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.
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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.
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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