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Multiplicity of the saturated special fiber ring of height two perfect ideals

Yairon Cid Ruiz (UGent)
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Abstract
Let R be a polynomial ring and let I subset of R be a perfect ideal of height two minimally generated by forms of the same degree. We provide a formula for the multiplicity of the saturated special fiber ring of I. Interestingly, this formula is equal to an elementary symmetric polynomial in terms of the degrees of the syzygies of I. Applying ideas introduced by Buse, D'Andrea, and the author, we obtain the value of the j-multiplicity of I and an effective method for determining the degree and birationality of rational maps defined by homogeneous generators of I.
Keywords
Applied Mathematics, General Mathematics, Saturated special fiber ring, rational and birational maps, j-multiplicity, syzygies, Rees algebra, symmetric algebra, special fiber ring, multiplicity, Hilbert-Burch theorem, local cohomology, CREMONA TRANSFORMATIONS, BIRATIONAL MAPS, EQUATIONS, ALGEBRAS

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Citation

Please use this url to cite or link to this publication:

MLA
Cid Ruiz, Yairon. “Multiplicity of the Saturated Special Fiber Ring of Height Two Perfect Ideals.” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 148, no. 1, 2020, pp. 59–70, doi:10.1090/proc/14693.
APA
Cid Ruiz, Y. (2020). Multiplicity of the saturated special fiber ring of height two perfect ideals. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 148(1), 59–70. https://doi.org/10.1090/proc/14693
Chicago author-date
Cid Ruiz, Yairon. 2020. “Multiplicity of the Saturated Special Fiber Ring of Height Two Perfect Ideals.” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 148 (1): 59–70. https://doi.org/10.1090/proc/14693.
Chicago author-date (all authors)
Cid Ruiz, Yairon. 2020. “Multiplicity of the Saturated Special Fiber Ring of Height Two Perfect Ideals.” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 148 (1): 59–70. doi:10.1090/proc/14693.
Vancouver
1.
Cid Ruiz Y. Multiplicity of the saturated special fiber ring of height two perfect ideals. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 2020;148(1):59–70.
IEEE
[1]
Y. Cid Ruiz, “Multiplicity of the saturated special fiber ring of height two perfect ideals,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 148, no. 1, pp. 59–70, 2020.
@article{8681012,
  abstract     = {{Let R be a polynomial ring and let I subset of R be a perfect ideal of height two minimally generated by forms of the same degree. We provide a formula for the multiplicity of the saturated special fiber ring of I. Interestingly, this formula is equal to an elementary symmetric polynomial in terms of the degrees of the syzygies of I. Applying ideas introduced by Buse, D'Andrea, and the author, we obtain the value of the j-multiplicity of I and an effective method for determining the degree and birationality of rational maps defined by homogeneous generators of I.}},
  author       = {{Cid Ruiz, Yairon}},
  issn         = {{0002-9939}},
  journal      = {{PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY}},
  keywords     = {{Applied Mathematics,General Mathematics,Saturated special fiber ring,rational and birational maps,j-multiplicity,syzygies,Rees algebra,symmetric algebra,special fiber ring,multiplicity,Hilbert-Burch theorem,local cohomology,CREMONA TRANSFORMATIONS,BIRATIONAL MAPS,EQUATIONS,ALGEBRAS}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{59--70}},
  title        = {{Multiplicity of the saturated special fiber ring of height two perfect ideals}},
  url          = {{http://dx.doi.org/10.1090/proc/14693}},
  volume       = {{148}},
  year         = {{2020}},
}

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