Abstract
The concept of generic anisotropy of a simplicial sphere was introduced by the authors as a key ingredient for a second proof of McMullen’s g-conjecture for simplicial spheres. In the present note we establish the generic anisotropy of all 1-dimensional simplicial spheres over an arbitrary field. We also prove that the determinant of the middle bilinear pairing of the generic Artinian reduction of the Stanley—Reisner ring determines the simplicial 1-sphere.
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Acknowledgements
We thank Karim Adiprasito and David Eisenbud for useful conversations. We benefited from experiments with the computer algebra program Macaulay2 [5]. This work is part of the Univ. of Ioannina Ph.D. thesis of V. P., financially supported by the Special Account for Research Funding (E.L.K.E.) of the University of Ioannina under the program with code number 82561 and title “Program of financial support for Ph.D. students and postdoctoral researchers”.
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Papadakis, S.A., Petrotou, V. The generic anisotropy of simplicial 1-spheres. Isr. J. Math. 254, 141–153 (2023). https://doi.org/10.1007/s11856-022-2391-6
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DOI: https://doi.org/10.1007/s11856-022-2391-6