Ivan Edgardo Pan

Bio: Ivan Edgardo Pan is an academic researcher. The author has contributed to research in topics: Cremona group & Group (mathematics). The author has an hindex of 1, co-authored 1 publications receiving 14 citations.

Cremona Maps of de Jonquières Type

Abstract: This paper is concerned with suitable generalizations of a plane de Jonquimap to higher dimensional space P n with n 3. For each given point of P n there is a subgroup of the entire Cre- mona group of dimension n consisting of such maps. We study both geometric and group-theoretical properties of this notion. In the case where n = 3 we describe an explicit set of generators of the group and give a homological characterization of a basic subgroup thereof.

Degree and birationality of multi-graded rational maps

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 the saturated 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.

Degree of rational maps and specialization

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 domain.

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

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.

Degree and birationality of multi-graded rational maps

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 the "saturated 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.

The Newton complementary dual revisited

Abstract: This work deals with the notion of Newton complementary duality as raised originally in the work of the second author and B. Costa. A conceptual revision of the main steps of the notion is accompli...