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Volumn 46, Issue 6, 2011, Pages 712-733

Quartic curves and their bitangents

Author keywords

Bitangents; Determinantal representations; Gale duality; Plane curves; Semidefinite programming; Sums of squares

Indexed keywords


EID: 79952484873     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2011.01.007     Document Type: Article
Times cited : (80)

References (31)
  • 1
    • 84966261323 scopus 로고
    • Linear systems of real quadratic forms
    • Calabi E. Linear systems of real quadratic forms. Proc. Amer. Math. Soc. 1964, 15:844-846.
    • (1964) Proc. Amer. Math. Soc. , vol.15 , pp. 844-846
    • Calabi, E.1
  • 2
    • 0012552611 scopus 로고
    • Algebraic Geometry and Theta Functions
    • American Math.~Society
    • Coble A. Algebraic Geometry and Theta Functions. Colloquium Publications 1929, vol. 10. American Math.~Society.
    • (1929) Colloquium Publications , vol.10
    • Coble, A.1
  • 3
    • 0040005962 scopus 로고
    • Note on the reduction of a ternary quantic to a symmetrical determinant
    • Dixon A.C. Note on the reduction of a ternary quantic to a symmetrical determinant. Cambridge Proc. 1902, 11:350-351.
    • (1902) Cambridge Proc. , vol.11 , pp. 350-351
    • Dixon, A.C.1
  • 5
    • 0003220018 scopus 로고
    • Point sets in projective spaces and theta functions
    • Dolgachev I., Ortland D. Point sets in projective spaces and theta functions. Astérisque 1988, (165).
    • (1988) Astérisque , Issue.165
    • Dolgachev, I.1    Ortland, D.2
  • 6
    • 0040691620 scopus 로고    scopus 로고
    • Three-phase solutions of the Kadomtsev-Petviashvili equation
    • Dubrovin B., Flickinger R., Segur H. Three-phase solutions of the Kadomtsev-Petviashvili equation. Stud. Appl. Math. 1997, 99:137-203.
    • (1997) Stud. Appl. Math. , vol.99 , pp. 137-203
    • Dubrovin, B.1    Flickinger, R.2    Segur, H.3
  • 7
    • 72049116654 scopus 로고
    • Determinantal representations of x4+y4+z4
    • Edge W.L. Determinantal representations of x4+y4+z4. Math. Proc. Cambridge Phil. Soc. 1938, 34:6-21.
    • (1938) Math. Proc. Cambridge Phil. Soc. , vol.34 , pp. 6-21
    • Edge, W.L.1
  • 8
    • 0034239481 scopus 로고    scopus 로고
    • The projective geometry of the Gale transform
    • Eisenbud D., Popescu S. The projective geometry of the Gale transform. J. Algebra 2000, 230:127-173.
    • (2000) J. Algebra , vol.230 , pp. 127-173
    • Eisenbud, D.1    Popescu, S.2
  • 9
    • 0004055957 scopus 로고
    • Algebraic curves
    • Addison-Wesley, reprinted in 1989
    • Fulton W. Algebraic curves. Advanced Book Classics 1969, Addison-Wesley, reprinted in 1989.
    • (1969) Advanced Book Classics
    • Fulton, W.1
  • 10
    • 79952486628 scopus 로고    scopus 로고
    • On covariants of plane quartic associated to its even theta characteristic
    • Amer. Math. Soc., Providence, RI, Proceedings of the Korea-Japan Conference in honor of Igor Dolgachev's 60th birthday
    • Gizatullin M. On covariants of plane quartic associated to its even theta characteristic. Contemp. Math. 2007, vol. 422:37-74. Amer. Math. Soc., Providence, RI.
    • (2007) Contemp. Math. , vol.422 , pp. 37-74
    • Gizatullin, M.1
  • 11
    • 0004290782 scopus 로고
    • Linear Algebra
    • Springer-Verlag, New York
    • Greub W. Linear Algebra. Graduate Texts in Mathematics 1975, vol. 23. Springer-Verlag, New York. fourth ed.
    • (1975) Graduate Texts in Mathematics , vol.23
    • Greub, W.1
  • 12
    • 84972568754 scopus 로고
    • Galois groups of enumerative problems
    • Harris J. Galois groups of enumerative problems. Duke Math. J. 1979, 46:685-724.
    • (1979) Duke Math. J. , vol.46 , pp. 685-724
    • Harris, J.1
  • 13
    • 34247216675 scopus 로고    scopus 로고
    • Linear matrix inequality representation of sets
    • Helton J.W., Vinnikov V. Linear matrix inequality representation of sets. Comm. Pure Appl. Math. 2007, 60:654-674.
    • (2007) Comm. Pure Appl. Math. , vol.60 , pp. 654-674
    • Helton, J.W.1    Vinnikov, V.2
  • 14
    • 72049086693 scopus 로고    scopus 로고
    • Detecting rigid convexity of bivariate polynomials
    • Henrion D. Detecting rigid convexity of bivariate polynomials. Linear Algebra Appl. 2010, 432:1218-1233.
    • (2010) Linear Algebra Appl. , vol.432 , pp. 1218-1233
    • Henrion, D.1
  • 15
    • 0040890189 scopus 로고
    • Über die Doppeltangenten der Curven vierter Ordnung
    • Hesse O. Über die Doppeltangenten der Curven vierter Ordnung. J. Reine Angew. Math. 1855, 49:279-332.
    • (1855) J. Reine Angew. Math. , vol.49 , pp. 279-332
    • Hesse, O.1
  • 16
    • 0000432495 scopus 로고
    • Ueber die Darstellung definiter Formen als Summe von Formenquadraten
    • Hilbert D. Ueber die Darstellung definiter Formen als Summe von Formenquadraten. Math. Ann. 1888, 32(3):342-350.
    • (1888) Math. Ann. , vol.32 , Issue.3 , pp. 342-350
    • Hilbert, D.1
  • 17
    • 34447612398 scopus 로고
    • Über den Verlauf der Abelschen Integrale bei den Kurven vierten Grades
    • Klein F. Über den Verlauf der Abelschen Integrale bei den Kurven vierten Grades. Math. Ann. 1876, 10:365-397.
    • (1876) Math. Ann. , vol.10 , pp. 365-397
    • Klein, F.1
  • 19
    • 79952489500 scopus 로고    scopus 로고
    • Discriminants and nonnegative polynomials, Preprint.
    • Nie, J., 2010. Discriminants and nonnegative polynomials, Preprint. arxiv:1002.2230.
    • (2010)
    • Nie, J.1
  • 20
    • 69949110756 scopus 로고    scopus 로고
    • The algebraic degree of semidefinite programming
    • Nie J., Ranestad K., Sturmfels B. The algebraic degree of semidefinite programming. Math. Program. Ser. A 2010, 122:379-405.
    • (2010) Math. Program. Ser. A , vol.122 , pp. 379-405
    • Nie, J.1    Ranestad, K.2    Sturmfels, B.3
  • 21
    • 79952484785 scopus 로고    scopus 로고
    • Computing linear matrix representations of Helton-Vinnikov curves. Preprint.
    • Plaumann, D., Sturmfels, B., Vinzant, C., 2010. Computing linear matrix representations of Helton-Vinnikov curves. Preprint. arxiv:1011.6057.
    • (2010)
    • Plaumann, D.1    Sturmfels, B.2    Vinzant, C.3
  • 22
    • 0039704132 scopus 로고
    • Solution d'une question fondamentale concernant la théorie générale des courbes
    • Plücker J. Solution d'une question fondamentale concernant la théorie générale des courbes. J. Reine Angew. Math. 1834, 12:105-108.
    • (1834) J. Reine Angew. Math. , vol.12 , pp. 105-108
    • Plücker, J.1
  • 23
    • 26844483821 scopus 로고    scopus 로고
    • Notes towards a constructive proof of Hilbert's theorem on ternary quartics
    • Amer. Math. Soc., Providence, RI, Quadratic Forms and Their Applications (Dublin, 1999)
    • Powers V., Reznick B. Notes towards a constructive proof of Hilbert's theorem on ternary quartics. Contemp. Math. 2000, vol. 272:209-227. Amer. Math. Soc., Providence, RI.
    • (2000) Contemp. Math. , vol.272 , pp. 209-227
    • Powers, V.1    Reznick, B.2
  • 25
    • 79952487313 scopus 로고    scopus 로고
    • Dualities in convex algebraic geometry, Rendiconti di Mathematica e delle sue Applicazioni (in press).
    • Rostalski, P., Sturmfels, B., Dualities in convex algebraic geometry, Rendiconti di Mathematica e delle sue Applicazioni (2011), (in press). arxiv:1006.4894.
    • (2011)
    • Rostalski, P.1    Sturmfels, B.2
  • 26
    • 0003926459 scopus 로고
    • A Treatise on the Higher Plane Curves: Intended as a Sequel to "A Treatise on Conic Sections", 3rd ed
    • Dublin, 1879; reprinted by Chelsea Publ. Co., New York,
    • Salmon, G., A Treatise on the Higher Plane Curves: Intended as a Sequel to "A Treatise on Conic Sections", 3rd ed., Dublin, 1879; reprinted by Chelsea Publ. Co., New York, 1960.
    • (1960)
    • Salmon, G.1
  • 28
    • 0039112020 scopus 로고
    • Eigenschaften der Curven vierten Grads rücksichtlich ihrer Doppeltangenten
    • Steiner J. Eigenschaften der Curven vierten Grads rücksichtlich ihrer Doppeltangenten. J. Reine Angew. Math. 1855, 49:265-272.
    • (1855) J. Reine Angew. Math. , vol.49 , pp. 265-272
    • Steiner, J.1
  • 29
    • 77954974609 scopus 로고
    • Seven points on a twisted cubic curve
    • White H.S. Seven points on a twisted cubic curve. Proc. Natl. Acad. Sci. USA 1915, 8:464-466.
    • (1915) Proc. Natl. Acad. Sci. USA , vol.8 , pp. 464-466
    • White, H.S.1
  • 30
    • 0008807868 scopus 로고
    • Self-adjoint determinantal representations of real plane curves
    • Vinnikov V. Self-adjoint determinantal representations of real plane curves. Math. Ann. 1993, 296(3):453-479.
    • (1993) Math. Ann. , vol.296 , Issue.3 , pp. 453-479
    • Vinnikov, V.1
  • 31
    • 0011529343 scopus 로고
    • Sur les différentes formes des courbes planes du quatrième ordre
    • Zeuthen H.G. Sur les différentes formes des courbes planes du quatrième ordre. Math. Ann. 1873, 7:408-432.
    • (1873) Math. Ann. , vol.7 , pp. 408-432
    • Zeuthen, H.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.