207
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Enumerative Algebraic Geometry of Conics

, &
Pages 701-728 | Published online: 31 Jan 2018

REFERENCES

  • M. Artin, Algebra, Prentice Hall, Englewood Cliffs, NJ, 1991.
  • D. Ayala and R. Cavalieri, Counting bitangents with stable maps, Expositiones Mathematicae 24 (2006) 307–336; also available at http://arxiv.org/abs/math.AG/0505139.
  • A. Bashelor, Enumerative Algebraic Geometry: Counting Conics, Trident Scholar Project Report, no. 330, United States Naval Academy, Annapolis, MD, 2005.
  • P. Candelas, X. de la Ossa, P. Green, and L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B 359 (1991) 21–74.
  • D. Cox, J. Little, and D. O'Shea, Using Algebraic Geometry, Graduate Texts in Mathematics, vol. 185, Springer-Verlag, New York, 1998.
  • H. Derksen and G. Kemper, Computational Invariant Theory, Encyclopaedia of Mathematical Sciences, vol. 130, Springer-Verlag, Berlin, 2002.
  • D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995.
  • D. Eisenbud, Projective geometry and homological algebra, in Computations in Algebraic Geometry with Macaulay 2, D. Eisenbud, D. R. Grayson, and M. Stillman, eds., Algorithms and Computation in Mathematics, vol. 8, Springer-Verlag, Berlin, 2002, 17–40.
  • D. Eisenbud, D. R. Grayson, and M. Stillman, eds., Computations in Algebraic Geometry with Macaulay 2, Algorithms and Computation in Mathematics, vol. 8, Springer-Verlag, Berlin, 2002.
  • W. Fulton, Introduction to Intersection Theory in Algebraic Geometry, CBMS Regional Conference Series in Mathematics, vol. 54, Conference Board of the Mathematical Sciences, Washington, DC, 1984.
  • W. Fulton, Intersection Theory, 2nd ed., Results in Mathematics and Related Areas, 3rd Series, A Series of Modern Surveys in Mathematics, vol. 2, Springer-Verlag, Berlin, 1998.
  • W. Fulton and R. MacPherson, Defining algebraic intersections, in Algebraic Geometry (Proc. Sympos., Univ. Tromsø, Tromsø, 1977), Lecture Notes in Mathematics, vol. 687, Springer-Verlag, Berlin, 1978, 1–30.
  • W. Fulton and R. Pandharipande, Notes on stable maps and quantum cohomology, in Algebraic geometry—Santa Cruz 1995, Proc. Sympos. Pure Math., vol. 62, American Mathematical Society, Providence, RI, 1997, 45–96.
  • I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, Mathematics: Theory & Applications, Birkhäuser, Boston, MA, 1994.
  • R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, Springer-Verlag, Berlin, 1977.
  • H. Hauser, The Hironaka theorem on resolution of singularities (or: A proof we always wanted to understand), Bull. Amer. Math. Soc. (N.S.) 40 (2003) 323–403.
  • S. Katz, Enumerative Geometry and String Theory, American Mathematical Society, Providence, RI, 2006.
  • S. Kleiman, Problem 15: Rigorous foundation of Schubert's enumerative calculus, in Mathematical Developments Arising from Hilbert Problems, Proc. Symp. Pure Math., vol. 28, American Mathematical Society, Providence, RI, 1976, 445–482.
  • S. Kleiman, Chasles's enumerative theory of conics: A historical introduction, in Studies in Algebraic Geometry, Mathematical Association of America Studies in Mathematics, vol. 20, Mathematical Association of America, Washington, DC, 1980, 117–138.
  • S. Kleiman, Intersection theory and enumerative geometry: A decade in review. With the collaboration of Anders Thorup on section 3, in Algebraic Geometry—Bowdoin 1985, Proc. Sympos. Pure Math., vol. 46, Part 2, American Mathematical Society, Providence, RI, 1987, 321–370.
  • S. L. Kleiman and D. Laksov, Schubert calculus, this Monthly 79 (1972) 1061–1082.
  • F. Ronga, A. Tognoli, and T. Vust, The number of conics tangent to 5 given conics: The real case, Rev. Mat. Univ. Complut. Madrid 10 (1997) 391–421.
  • J.-P. Serre, Algèbre Locale. Multiplicités, 2nd ed., Lecture Notes in Mathematics, vol. 11, Springer-Verlag, Berlin, 1965.
  • K. E. Smith, L. Kahanpää, P. Kekäläinen, and W. Traves, An Invitation to Algebraic Geometry, Universitext, Springer-Verlag, New York, 2000.
  • F. Soddy, The kiss precise, Nature 137 (1936) 1021.
  • F. Sottile, Enumerative geometry for real varieties, in Algebraic geometry—Santa Cruz 1995, Proc. Sympos. Pure Math., vol. 62, American Mathematical Society, Providence, RI, 1997, 435–447.
  • F. Sottile, From enumerative geometry to solving systems of polynomials equations, in Computations in Algebraic Geometry with Macaulay 2, D. Eisenbud, D. R. Grayson, and M. Stillman, eds., Algorithms and Computation in Mathematics, vol. 8, Springer-Verlag, Berlin, 2002, 101–129.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.