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Abdallah, N., et al. “Hilbert functions and Jordan type of Perazzo Artinian algebras.” In: Lefschetz Properties, 59-80. Vol. 59 of Springer INdAM Ser.. Singapore: Springer, 2024. Cited on 37.Search in Google Scholar
Altafi, N., et al. “Artinian Gorenstein algebras having binomial Macaulay dual generator.” In preparation. Cited on 42.Search in Google Scholar
Billera, L. J., and C. W. Lee. “A proof of the Sufficiency of McMullen’s Conditions for f-Vectors of Simplicial Convex Polytopes.” J. Combin. Theory Ser. A 31 (1981): 237-255. Cited on 22.Search in Google Scholar
Chern, S.-S. “On a Generalization of Kähler Geometry.” In: R. H. Fox, et al. (eds.), Algebraic Geometry and Topology, 103-124. Princeton, NJ: Princeton Univ. Press, 1951. Cited on 11.Search in Google Scholar
Cook, D. II. “The Lefschetz properties of monomial complete intersections in positive characteristic.” J. Algebra 369 (2012): 42-58. Cited on 21.Search in Google Scholar
Deligne, P. “La conjecture de Weil. II.” Inst. Hautes Études Sci. Publ. Math. no. 52 (1980): 137-252. Cited on 11.Search in Google Scholar
DiPasquale, M., T. Nguy˜ên, and A. Seceleanu. “Duality for asymptotic invariants of graded families.” Adv. Math. 430 (2023): paper no. 109208. Cited on 28.Search in Google Scholar
Eisenbud, D. Commutative Algebra: With a View Toward Algebraic Geometry. Graduate Texts in Mathematics, Vol. 150. New York: Springer-Verlag, 1995. Cited on 28.Search in Google Scholar
Geramita, A. V. “Inverse systems of fat points: Waring’s problem, secant varieties of Veronese varieties and parameter spaces for Gorenstein ideals.” In: The Curves Seminar at Queen’s, 2-114. Vol. 102 of Queen’s Papers in Pure and Appl. Math. Kingston, ON: Queen’s Univ., 1996. Cited on 28 and 31.Search in Google Scholar
Gondim, R. “On higher Hessians and the Lefschetz properties.” J. Algebra 489 (2017): 241-263. Cited on 36.Search in Google Scholar
Gondim, R., and F. Russo. “Cubic hypersurfaces with vanishing Hessian.” J. Pure Appl. Algebra 219 (2015): 779-806. Cited on 44.Search in Google Scholar
Grayson, D., and M. Stillman. Macaulay2, a software system for research in algebraic geometry. Available at: http://www2.macaulay2.com. Cited on 19.Search in Google Scholar
Harima, T., et al. The Lefschetz Properties. Vol. 2080 of Lecture Notes in Mathematics. Heidelberg: Springer, 2013. Cited on 7, 8 and 27.Search in Google Scholar
Harima, T., and J. Watanabe. “The strong Lefschetz property for Artinian algebras with non-standard grading.” J. Algebra 311 (2007): 511-537. Cited on 19.Search in Google Scholar
Herzog, J., and D. Popescu. “The strong Lefschetz property and simple extensions.” arXiv:math/05065537. Cited on 21.Search in Google Scholar
Hodge, W. V. D. The Theory and Applications of Harmonic Integrals. 2nd ed. London: Cambridge Univ. Press, 1952. Cited on 11.Search in Google Scholar
Iarrobino, A., P. Macias Marques, and C. McDaniel. “Artinian algebras and Jordan type.” J. Commut. Algebra 14, no. 3 (2022): 365-414. Cited on 26.Search in Google Scholar
Iarrobino, A., C. McDaniel, and A. Seceleanu. “Connected sums of graded Artinian Gorenstein algebras and Lefschetz properties.” J. Pure Appl. Algebra 226, no. 1 (2022): 106787. Cited on 37, 38 and 39.Search in Google Scholar
Iarrobino, A., P. Macias Marques, C. McDaniel, A. Seceleanu, and J. Watanabe. “Cohomological blow ups of graded Artinian Gorenstein algebras along surjective maps.” Int. Math. Res. Not. IMRN 2023, no. 7 (2023): 5816-5886. Cited on 8, 37, 43, 44 and 45.Search in Google Scholar
Ikeda, H. “Results on Dilworth and Rees numbers of Artinian local rings.” Jpn. J. Math. (N.S.) 22, no. 1 (1996): 147-158. Cited on 36.Search in Google Scholar
Lefschetz, S. L’Analysis Situs et la Géometrie Algébrique. Paris: Gauthier-Villars, 1924. Reprinted in: Selected Papers. New York: Chelsea, 1971. Cited on 11.Search in Google Scholar
Lefschetz, S. “Reminiscences of a mathematical immigrant in the United States.” Amer. Math. Monthly 77 (1970): 344-350. Cited on 11.Search in Google Scholar
Lindsey, M. “A class of Hilbert series and the strong Lefschetz property.” Proc. Amer. Math. Soc. 139 (2011): 79-92. Cited on 21.Search in Google Scholar
Macaulay, F. S. The Algebraic Theory of Modular Systems. Cambridge Mathematical Library. Cambridge: Cambridge Univ. Press, 1994. Cited on 29.Search in Google Scholar
Maeno, T., and J. Watanabe. “Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials.” Illinois J. Math. 53, no. 2 (2009): 591-603. Cited on 28 and 35.Search in Google Scholar
McMullen, P. “The numbers of faces of simplicial polytopes.” Israel J. Math. 9 (1971): 559-570. Cited on 21.Search in Google Scholar
Nicklasson, L. “The strong Lefschetz property of monomial complete intersections in two variables.” Collect. Math. 69, no. 3 (2018): 359-375. Cited on 21.Search in Google Scholar
Perazzo, U. “Sulle varietà cubiche la cui hessiana svanisce identicamente.” Giorn. Mat. Battaglini 38 (1900): 337-354. Cited on 44.Search in Google Scholar
Reid, L., L. Roberts, and M. Roitman. “On complete intersections and their Hilbert functions.” Canad. Math. Bull. 34 (1991): 525-535. Cited on 21.Search in Google Scholar
Robles, C. “Linear structures of Hodge theory.” Available at: https://sites.math.duke.edu/~robles/21.02-ICERM.pdf. Cited on 22.Search in Google Scholar
Stanley, R. “The number of faces of a simplicial convex polytope.” Adv. Math. 35 (1980): 236-238. Cited on 22.Search in Google Scholar
Stanley, R. “Combinatorial applications of the hard Lefschetz theorem.” In: Proc. Int. Congr. Math., Warsaw, Aug. 16-24, 1983, 447-453. Warsaw: PWN-Polish Scientific Publishers, 1984. Cited on 21.Search in Google Scholar
Watanabe, J. “The Dilworth number of Artinian rings and finite posets with rank function.” In: Commutative Algebra and Combinatorics, Vol. 11 of Adv. Stud. Pure Math. Amsterdam: North-Holland, 1987. Cited on 21.Search in Google Scholar