Abstract
The main purpose of this paper is to show that for the class of standard graded fiber product rings, the lower and upper bounds of the Multiplicity conjecture can be improved. In certain cases, explicit formulas for the multiplicity of the graded fiber product ring are determined.
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Acknowledgements
The authors would like to thank Maria A. S. Ruas and Fábio Natali for the kind comments and suggestions for the improvement of the paper. Also, the authors are grateful to the anonymous referee for her/his careful reading of this manuscript and the many deep suggestions and corrections. This work was done during the Posdoctoral of the first author in Universidade de São Paulo, ICMC-Brazil, 2021–2022. The first author also thanks the Universidade Tecnológica Federal do Paraná- Guarapuava- Brazil.
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The authors were partially supported by CNPq-Brazil, grant 421440/2016-3.
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Freitas, T.H., Jorge-Pérez, V.H. Bounds for Multiplicities of the Graded Fiber Product Ring. Bull Braz Math Soc, New Series 53, 925–940 (2022). https://doi.org/10.1007/s00574-022-00289-6
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DOI: https://doi.org/10.1007/s00574-022-00289-6