On the hypersurfaces contained in their Hessian
Abstract
Keywords
Mathematics Subject Classification (2010)
References
Beltrametti, Mauro C. et all. Lectures on curves, surfaces and projective varieties. Zürich: European Mathematical Society (EMS), 2009.
Ciliberto, Ciro. "Algebraic hypersurfaces with parabolic points and related Hessians." Rend. Accad. Naz Sci. XL Mem. Mat. 4 (1979/80): 25-42.
Ciliberto, Ciro and Edoardo Sernesi. "Singularities of the theta divisor and congruences of planes." J. Algebraic Geom. 1, no. 2 (1992): 231-250.
De Poi, Pietro. "On first order congruences of lines of P4 with a fundamental curve." Manuscripta Math. 106, no. 1 (2001): 101-116.
De Poi, Pietro. "Threefolds in P5 with one apparent quadruple point." Comm. Algebra 31, no. 4 (2003): 1927-1947.
De Poi, Pietro. "Congruences of lines with one-dimensional focal locus." Port. Math. (N.S.) 61, no. 3 (2004): 329-338.
De Poi, Pietro. "On first order congruences of lines in P4 with irreducible fundamental surface." Math. Nachr. 278, no. 4 (2005): 363-378.
De Poi, Pietro. "On first order congruences of lines in P4 with generically nonreduced fundamental surface." Asian J. Math. 12, no. 1 (2008): 55-64.
De Poi, Pietro, Roberta Di Gennaro, and Giovanna Ilardi. "On varieties with higher osculating defect." Rev. Mat. Iberoam. 29, no. 4 (2013): 1191-1210.
De Poi, Pietro and Giovanna Ilardi. "On higher Gauss maps." J. Pure Appl. Algebra 219, no. 11 (2015): 5137-5148.
Franchetta, Alfredo. "Sulle forme algebriche di S4 aventi l’hessiana indeterminata." Rend. Mat. e Appl. (5) 14 (1954): 252-257.
Franchetta, Alfredo. "Forme algebriche sviluppabili e relative hessiane." Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 10 (1951): 386-389.
Gondim, Rodrigo and Francesco Russo. "On cubic hypersurfaces with vanishing hessian." J. Pure Appl. Algebra 219, no. 4 (2015): 779-806.
Gondim, Rodrigo. "On higher hessians and the Lefschetz properties." J. Algebra 489 (2017): 241-263.
Gondim, Rodrigo and Giuseppe Zappalà. "Lefschetz properties for artinian Gorenstein algebras presented by quadrics." Proc. Amer. Math. Soc. 146, no. 3 (2018): 993-1003.
Griffiths, Phillip and Joseph Harris. Principles of algebraic geometry. New York: John Wiley & Sons, Inc., 1994.
Griffiths, Phillip and Joseph Harris. "Algebraic geometry and local differential geometry." Ann. Sci. École Norm. Sup. (4) 12, no. 3 (1979): 355-452.
Hartshorne, Robin. Algebraic geometry. Vol. 52 of Graduate Texts in Mathematics. New York-Heidelberg: Springer-Verlag, 1977.
Segre, Beniamino. "Bertini forms and Hessian matrices." J. London Math. Soc. 26 (1951): 164-176.
Segre, Corrado . "Un’ osservazione sui sistemi di rette degli spazii superiori." Rend. Circ. Mat. Palermo 2 (1888): 148-149.
Segre, Corrado. "Preliminari di una teoria delle varietà luoghi di spazi." Rend. Circ. Mat. Palermo 30 (1910): 87-121.
Watanabe, Junzo. "A remark on the Hessian of homogeneous polynomials." In The Curves Seminar at Queen’s, vol. XIII. Vol. 119 of Queen’s Papers in Pure and Applied Mathematics, 171-178. Kingston: Queen’s University, 2000.
Watanabe, Junzo. "On the theory of Gordan-Noether on homogeneous forms with zero hessian." Proc. Sch. Sci. Tokay Univ., 49 (2014): 1-21.
Watanabe, Junzo. "On the theory of Gordan-Noether on homogeneous forms with zero hessian." arXiv (2017): arXiv:1703.07624.
Zak, Fyodor L. "Determinants of projective varieties and their degrees." In Algebraic transformation groups and algebraic varieties. Vol. 132 of Encyclopaedia Math. Sci., 207-238. Berlin: Springer, 2004.
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