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Original Articles

On the universal scheme of r-relative clusters of a family

Pages 2708-2725 | Received 03 Aug 2014, Published online: 20 Oct 2016

References

  • Alberich-Carramiñana, M., Roé, J. (2005). Enriques diagrams and adjacency of planar curve singularities. Canad. J. Math. 57(1):3–16.
  • Casas-Alvero, E. (2000). Singularities of Plane Curves. London Mathematical Society Lecture Note Series, Vol. 276. Cambridge: Cambridge University Press.
  • De Poi, P. (2003). Threefolds in ℙ5 with one apparent quadruple point. Commun. Algebra 31(4):1927–1947.
  • Fernández de Bobadilla, J. (2005). Moduli spaces of polynomials in two variables. Mem. Am. Math. Soc. 173(817):x+136.
  • Grothendieck, A. (1995a). Technique de descente et théorèmes d’existence en géométrie algébrique. II. Le théorème d’existence en théorie formelle des modules’. Séminaire N. Bourbaki, 1958–1960, Vol. 5. Paris: Société Mathématique de France Exp. No. 195, pp. 369–390. Available at: http://www.numdam.org/item?id=SB_1958-1960__5__369_0.
  • Grothendieck, A. (1995b). Techniques de construction et théorèmes d’existence en géométrie algébrique. IV. Les schémas de Hilbert. Séminaire N. Bourbaki, 1960–1961, Vol. 6. Paris: Société Mathématique de France, Exp. No. 221, pp. 249–276. Available at: http://www.numdam.org/item?id=SB_1960-1961__6__249_0.
  • Grothendieck, A. (1995c). Technique de descente et théorèmes d’existence en géométrie algébrique. VI. Les schémas de Picard: propriétés générales. Séminaire N. Bourbaki, 1961–1962, Vol. 7. Paris: Société Mathématique de France, Exp. No. 236, pp. 221–243. Available at: http://www.numdam.org/item?id=SB_1961-1962__7__221_0.
  • Harbourne, B. (1988). Iterated Blow-ups and Moduli for Rational Surfaces. Algebraic Geometry (Sundance, UT, 1986), Lecture Notes in Mathematics, Vol. 1311. Berlin: Springer, pp. 101–117.
  • Hartshorne, R. (1977). Algebraic Geometry. Graduate Texts in Mathematics, Vol. 52. New York-Heidelberg: Springer-Verlag.
  • Keel, S. (1993). Intersection theory of linear embeddings. Trans. Am. Math. Soc. 335(1):195–212.
  • Kleiman, S. L. (1981). Multiple-point formulas. I. Iteration. Acta Math. 147(1–2):13–49.
  • Kleiman, S. L. (2005). The Picard Scheme. Fundamental Algebraic Geometry, Mathematical Surveys and Monographs, Vol. 123. Providence, RI: American Mathematical Society, pp. 235–321.
  • Kleiman, S. L., Piene, R. (1999). Enumerating Singular Curves on Surfaces. Algebraic Geometry: Hirzebruch 70 (Warsaw, 1998), Vol. 241. Providence, RI: Contemporary Mathematics - American Mathematical Society, pp. 209–238.
  • Kleiman, S. L., Piene, R. (2004). Node polynomials for families: methods and applications. Math. Nachr. 271:69–90.
  • Kleiman, S. L., Piene, R. (2011). Enriques diagrams, arbitrarily near points, and Hilbert schemes. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 22(4):411–451 (Appendix B by Ilya Tyomkin).
  • Nitsure, N. (2005). Construction of Hilbert and Quot Schemes. Fundamental Algebraic Geometry, Mathematical Surveys and Monographs, Vol. 123. Providence, RI: American Mathematical Society, pp. 105–137.
  • Paxia, G. (1991). On flat families of fat points. Proc. Am. Math. Soc. 112(1):19–23.
  • Ran, Z. (2005). Geometry on nodal curves. Compos. Math. 141(5):1191–1212.
  • Roé, J. (2001a). On the existence of plane curves with imposed multiple points. J. Pure Appl. Algebra 156(1):115–126.
  • Roé, J. (2001b). Conditions imposed by tacnodes and cusps. Trans. Am. Math. Soc. 353(12):4925–4948 (electronic).
  • Roé, J. (2004). Varieties of clusters and Enriques diagrams. Math. Proc. Cambridge Philos. Soc. 137(1):69–94.
  • Stacks Project Authors, T. (2015). Stacks project. Available at: http://stacks.math.columbia.edu.

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