Degree and birationality of multi‐graded rational maps
- Author
- Laurent Busé, Yairon Cid Ruiz (UGent) and Carlos D'Andrea
- Organization
- Abstract
- We give formulas and effective sharp bounds for the degree of multi-graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties. We also extend the Jacobian dual criterion to the multi-graded setting. Our approach is based on the study of blow-up algebras, including syzygies, of the ideal generated by the defining polynomials of the rational map. A key ingredient is a new algebra that we call thesaturated special fiber ring, which turns out to be a fundamental tool to analyze the degree of a rational map. We also provide a very effective birationality criterion and a complete description of the equations of the associated Rees algebra of a particular class of plane rational maps.
- Keywords
- General Mathematics, 13D02 (primary), 14E05, 13D45, 13P99 (secondary), CREMONA TRANSFORMATIONS, APPROXIMATION COMPLEXES, EFFECTIVE CRITERIA, LOCAL COHOMOLOGY, EQUATIONS, ALGEBRAS, SYZYGIES, INTERSECTION, MULTIPLICITY, FIBERS
Downloads
-
multgradedmaps-revised.pdf
- full text (Accepted manuscript)
- |
- open access
- |
- |
- 599.35 KB
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8681010
- MLA
- Busé, Laurent, et al. “Degree and Birationality of Multi‐graded Rational Maps.” PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, vol. 121, no. 4, 2020, pp. 743–87, doi:10.1112/plms.12336.
- APA
- Busé, L., Cid Ruiz, Y., & D’Andrea, C. (2020). Degree and birationality of multi‐graded rational maps. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 121(4), 743–787. https://doi.org/10.1112/plms.12336
- Chicago author-date
- Busé, Laurent, Yairon Cid Ruiz, and Carlos D’Andrea. 2020. “Degree and Birationality of Multi‐graded Rational Maps.” PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY 121 (4): 743–87. https://doi.org/10.1112/plms.12336.
- Chicago author-date (all authors)
- Busé, Laurent, Yairon Cid Ruiz, and Carlos D’Andrea. 2020. “Degree and Birationality of Multi‐graded Rational Maps.” PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY 121 (4): 743–787. doi:10.1112/plms.12336.
- Vancouver
- 1.Busé L, Cid Ruiz Y, D’Andrea C. Degree and birationality of multi‐graded rational maps. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. 2020;121(4):743–87.
- IEEE
- [1]L. Busé, Y. Cid Ruiz, and C. D’Andrea, “Degree and birationality of multi‐graded rational maps,” PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, vol. 121, no. 4, pp. 743–787, 2020.
@article{8681010,
abstract = {{We give formulas and effective sharp bounds for the degree of multi-graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties. We also extend the Jacobian dual criterion to the multi-graded setting. Our approach is based on the study of blow-up algebras, including syzygies, of the ideal generated by the defining polynomials of the rational map. A key ingredient is a new algebra that we call thesaturated special fiber ring, which turns out to be a fundamental tool to analyze the degree of a rational map. We also provide a very effective birationality criterion and a complete description of the equations of the associated Rees algebra of a particular class of plane rational maps.}},
author = {{Busé, Laurent and Cid Ruiz, Yairon and D'Andrea, Carlos}},
issn = {{0024-6115}},
journal = {{PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY}},
keywords = {{General Mathematics,13D02 (primary),14E05,13D45,13P99 (secondary),CREMONA TRANSFORMATIONS,APPROXIMATION COMPLEXES,EFFECTIVE CRITERIA,LOCAL COHOMOLOGY,EQUATIONS,ALGEBRAS,SYZYGIES,INTERSECTION,MULTIPLICITY,FIBERS}},
language = {{eng}},
number = {{4}},
pages = {{743--787}},
title = {{Degree and birationality of multi‐graded rational maps}},
url = {{http://doi.org/10.1112/plms.12336}},
volume = {{121}},
year = {{2020}},
}
- Altmetric
- View in Altmetric
- Web of Science
- Times cited: