Linear balls and the multiplicity conjecture |
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Authors: | Takayuki Hibi Pooja Singla |
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Institution: | 1. Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan;2. FB Mathematik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany |
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Abstract: | A linear ball is a simplicial complex whose geometric realization is homeomorphic to a ball and whose Stanley–Reisner ring has a linear resolution. It turns out that the Stanley–Reisner ring of the sphere which is the boundary complex of a linear ball satisfies the multiplicity conjecture. A class of shellable spheres arising naturally from commutative algebra whose Stanley–Reisner rings satisfy the multiplicity conjecture will be presented. |
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