Multiplicity of the saturated special fiber ring of height two perfect ideals
Abstract
Let $R$ be a polynomial ring and $I \subset R$ 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 in arXiv:1805.05180, we obtain the value of the jmultiplicity of $I$ and an effective method for determining the degree and birationality of rational maps defined by homogeneous generators of $I$.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 arXiv:
 arXiv:1807.03189
 Bibcode:
 2018arXiv180703189C
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 13A30 (Primary);
 14E05;
 13D02;
 13D45 (Secondary)
 EPrint:
 to appear in Proc. Amer. Math. Soc