Degree of rational maps and specialization

Yairon Cid Ruiz and Aron Simis

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Submission date: 07. Aug. 2020
Bibtex
MSC-Numbers: 14E05, 13D02, 13D45, 13P99
Link to arXiv: See the arXiv entry of this preprint.
DOI number (of the published article): 10.1093/imrn/rnaa183

Abstract:
One considers the behavior of the degree of a rational map under specialization of the coefficients of the defining linear system. The method rests on the classical idea of Kronecker as applied to the context of projective schemes and their specializations. For the theory to work one is led to develop the details of rational maps and their graphs when the ground ring of coefficients is a Noetherian integral domain.