]. M. Atm, I. G. Atiyah, and . Macdonald, Introduction to commutative algebra, 1969.

]. V. Bar and . Baranovski, The variety of pairs of commuting nilpotent matrices is irreducible, Transform. Groups, pp.3-8, 2001.

]. R. Bas00 and . Basili, On the irreducibility of varieties of commuting matrices, J. Pure Appl. Algebra, vol.149, pp.107-120, 2000.

]. R. Bas03 and . Basili, On the irreducibility of commuting varieties of nilpotent matrices, J. Algebra, vol.268, pp.58-80, 2003.

]. J. Ber and . Bertin, The punctual Hilbert scheme: an introduction In: Geometric methods in representation theory. I, 1-102, 2012.

]. M. Bo and . Boos, Non-reductive conjugation on the nilpotent cone, Algebr. Represent . Theory, vol.17, pp.1683-1706, 2014.

]. J. Br and . Briançon, Description de Hilb n C{x; y}, Invent. Math, vol.41, pp.45-89, 1977.

]. M. Bu and . Bulois, Composantes irréductibles de la variété commutante nilpotente d'une algèbre de Lie symétrique semi-simple, Annales de l'institut Fourier, pp.59-96, 2009.

J. Cheah, Cellular decompositions for nested Hilbert schemes of points, Pacific Journal of Mathematics, vol.183, issue.1, pp.39-90, 1998.
DOI : 10.2140/pjm.1998.183.39

J. Cheah, The virtual Hodge polynomials of nested Hilbert schemes and related varieties, Mathematische Zeitschrift, vol.227, issue.3, pp.479-504, 1998.
DOI : 10.1007/PL00004387

. E. Ce-]-p, L. Chaput, and . Evain, On the equivariant cohomology of Hilbert schemes of points in the plane

]. D. Eis and . Eisenbud, Commutative algebra With a view toward algebraic geometry, Graduate Texts in Mathematics, p.150, 1995.

D. Eisenbud and J. Harris, The geometry of schemes, Graduate Texts in Mathematics, 2000.

S. [. Ellingsrud and . Strømme, On the homology of the Hilbert scheme of points in the plane, Inventiones Mathematicae, vol.298, issue.No. 9, pp.343-352, 1987.
DOI : 10.1007/BF01389419

]. L. Ev and . Evain, Irreducible components of the equivariant punctual Hilbert schemes, Adv. Math, vol.185, issue.2, pp.328-346, 2004.

]. M. Ge and . Gerstenhaber, On dominance and varieties of commuting matrices, Annals Math, vol.73, pp.324-348, 1961.

]. V. Gi and . Ginzburg, Lectures on Nakajima's Quiver Varieties In: Geometric methods in representation theory. I, pp.145-219, 2012.

. S. Gr, G. Goodwin, and . Roehrle, On commuting varieties of nilradicals of Borel subalgebras of reductive Lie algebras, Proc. Edinb, pp.58-169, 2015.

]. I. Gr and . Grojnowski, Instantons and affine algebras. I. The Hilbert scheme and vertex operators, Math. Res. Lett, vol.3, issue.2, pp.275-291, 1996.

]. A. Gro and . Grothendieck, Techniques de construction et théorèmes d'existence en géométrie algébrique. IV. Les schémas de Hilbert. (French) [Construction techniques and existence theorems in algebraic geometry, IV. Hilbert schemes] Séminaire Bourbaki, pp.249-276, 1995.

A. Grothendieck, Techniques de construction en géométrie analytique . IV. Formalisme général des foncteurs représentables. Séminaire Henri Cartan, 1960.

. Hm-]-m, B. Haiman, and . Sturmfels, Multigraded Hilbert schemes, J. Algebraic Geom, vol.13, issue.4, pp.725-769, 2004.

]. S. Kee and . Keel, Functorial construction of Le Barz's triangle space with applications, Trans. Amer. Math. Soc, vol.335, issue.1, pp.213-229, 1993.

]. M. Le and . Lehn, Chern classes of tautological sheaves on Hilbert schemes of points on surfaces, Invent. Math, vol.136, issue.1, pp.157-207, 1999.

. D. Mfk, J. Mumford, F. Fogarty, and . Kirwan, Geometric invariant theory third edition, Ergeb. Math. Grenzgeb, issue.2, 1994.

]. H. Na and . Nakajima, Lectures on Hilbert schemes of points on surfaces, 1999.

]. D. Pa and . Panyushev, The Jacobian modules of a representation of a Lie algebra and geometry of commuting varieties, Compositio Math, vol.94, pp.181-199, 1994.

]. V. Po and . Popov, Irregular and singular loci of commuting varieties, Transform . Groups, pp.819-837, 2008.

]. A. Pr and . Premet, Nilpotent commuting varieties of reductive Lie algebras, Invent. Math, vol.154, pp.653-683, 2003.

]. S. St and . Stromme, Elementary introduction to representable functors and Hilbert schemes, Parameter spaces, pp.179-198, 1996.

. W. Ta-]-h, A. C. Turnbull, and . Aitken, An Introduction to the theory of canonical matrices, 1961.

[. Tauvel and R. W. Yu, Lie algebras and algebraic groups, 2005.

]. E. Zo and . Zoque, On the variety of almost commuting nilpotent matrices, Transform. Groups, pp.483-501, 2010.