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Articles

Biduality and reflexivity in positive characteristic

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Pages 3899-3931 | Received 06 Apr 2020, Accepted 25 Feb 2022, Published online: 26 Mar 2022

References

  • Akivis, M. A., Goldberg, V. V. (2004). Differential Geometry of Varieties with Degenerate Gauss Maps. Vol. 18: CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. New York: Springer-Verlag.
  • Bosma, W., Cannon, J., Playoust, C. (1997). The Magma algebra system I: The user language. J. Symbolic Comput. 24(3–4):235–265. DOI: 10.1006/jsco.1996.0125.
  • Crespo, T., Hajto, Z. (2011). Algebraic Groups and Differential Galois Theory. Vol. 122: Graduate Studies in Mathematics. Providence, RI: American Mathematical Society.
  • da Silva, A. C. (2001). Lectures on Symplectic Geometry. Vol. 1764: Lecture Notes in Mathematics. 1st ed. corr., 2nd printing edition, 2001. Berlin-Heidelberg: Springer.
  • Deligne, P., Katz, N., Katz, N. M. (1973). Groupes de Monodromie en Géométrie Algébrique. II: Séminaire de Géométrie Algébrique du Bois-Marie 1967–1969 (SGA 7 II), Dirigé par. Vol. 340: Lecture Notes in Mathematics. Berlin; New York: Springer-Verlag.
  • Eisenbud, D. (1995). Commutative Algebra. New York: Springer-Verlag. With a view toward algebraic geometry.
  • Fukasawa, S., Kaji, H. (2007). The separability of the Gauss map and the reflexivity for a projective surface. Math. Z. 256(4):699–703. DOI: 10.1007/s00209-006-0085-0.
  • Gelfand, I. M., Kapranov, M. M. (1993). On the dimension and degree of the projective dual variety: A q-analog of the Katz-Kleiman formula. In The Gelfand Mathematical Seminars, 1990–1992. Boston, MA: Birkhäuser, pp. 27–33.
  • Gelfand, I. M., Kapranov, M., Zelevinsky, A. (2008). Discriminants, Resultants, and Multidimensional Determinants. Modern Birkhäuser Classics. Boston, MA: Birkhäuser.
  • Goss, D. (1996). Basic Structures of Function Field Arithmetic. Vol. 35: Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]. Berlin: Springer-Verlag.
  • Hartshorne, R. (1977). Algebraic Geometry. Graduate Texts in Mathematics, No. 52. New York: Springer-Verlag.
  • Hasse, H. (1937). Noch eine Begründung der Theorie der höheren Differentialquotienten in einem algebraischen Funktionenkörper einer Unbestimmten. (Nach einer brieflichen Mitteilung von F.K. Schmidt in Jena). Journal Für Die Reine Und Angewandte Mathematik 177:215–223.
  • Hefez, A. (1989). Nonreflexive curves. Compos. Math. 69(1):3–35.
  • Hefez, A., Kleiman, S. L. (1985). Notes on the duality of projective varieties. In Geometry Today (Rome, 1984). Vol. 60: Progress in Mathematics. Boston, MA: Birkhäuser Boston, pp. 143–183.
  • Hida, H. (2012). Geometric Modular Forms and Elliptic Curves. 2nd ed. Hackensack, NJ: World Scientific Publishing Co. Pte. Ltd.
  • Hidalgo, R. A., Kontogeorgis, A., Leyton-Álvarez, M., Paramantzoglou, P. (2017). Automorphisms of generalized Fermat curves. J. Pure Appl. Algebra 221(9):2312–2337. DOI: 10.1016/j.jpaa.2016.12.011.
  • Holme, A. (1979). On the dual of a smooth variety. In Algebraic Geometry (Proc. Summer Meeting, Univ. Copenhagen, Copenhagen, 1978). Vol. 732: Lecture Notes in Mathematics. Berlin: Springer, pp. 144–156.
  • Hosgood, T. (2016). An introduction to varieties in weighted projective space. 8 April.
  • Kaji, H. (1992). On the inseparable degrees of the Gauss map and the projection of the conormal variety to the dual of higher order for space curves. Math. Ann. 292(1):529–532. DOI: 10.1007/BF01444633.
  • Kleiman, S., Piene, R. (1991). On the inseparability of the Gauss map. In Enumerative algebraic geometry (Copenhagen, 1989). Vol. 123: Contemporary Mathematics. Providence, RI: American Mathematical Society, pp. 107–129.
  • Kleiman, S. L. (1977). The enumerative theory of singularities. pp. 297–396.
  • Kleiman, S. L. (1986). Tangency and duality. In Proceedings of the 1984 Vancouver Conference in Algebraic Geometry. Providence, RI: American Mathematical Society, pp. 163–225.
  • Milne, J. S. (2013). Lectures on etale cohomology (v2.21). www.jmilne.org/math/
  • Schmidt, F. K. (1939). Die Wronskische Determinante in beliebigen differenzierbaren Funktionenkörpern. Math. Z. 45(1):62–74. DOI: 10.1007/BF01580273.
  • Shafarevich, I. R. (1994). Basic Algebraic Geometry. 1. Varieties in Projective Space. 2nd ed. Berlin: Springer-Verlag. Translated from the 1988 Russian edition and with notes by Miles Reid.
  • Shafarevich, I.R. (1994). Basic Algebraic Geometry, 2nd ed. Berlin: Springer-Verlag.
  • Tevelev, E. A. (2003). Projectively dual varieties. J. Math. Sci. 117(6):4585–4732. DOI: 10.1023/A:1025366207448.
  • Vakil, R. (2017). The Rising Sea. http://math.stanford.edu/∼vakil/216blog/FOAGnov1817public.pdf
  • Wallace, A. H. (1956). Tangency and duality over arbitrary fields. Proc. London Math. Soc. s3-6(3):321–342. DOI: 10.1112/plms/s3-6.3.321.

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