Author
A. V. Doria
Bio: A. V. Doria is an academic researcher from Universidade Federal de Sergipe. The author has contributed to research in topics: Jacobian matrix and determinant & Invariant (mathematics). The author has an hindex of 1, co-authored 1 publications receiving 70 citations.
Papers
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TL;DR: In this article, the Jacobian dual rank of a rational map is defined and attains its maximal possible value, and it is shown that a rational/birational map is irreducible if and only if it attains this value.
82 citations
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TL;DR: In this paper, the authors deal with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus.
Abstract: This work deals with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus. A particular emphasis is given to both weighted homogeneous and homogeneous polynomials, allowing to introduce new families of free divisors not coming from either hyperplane arrangements or discriminants in singularity theory.
56 citations
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TL;DR: In this paper, the authors consider reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus.
Abstract: One deals with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus. A particular emphasis is given to both weighted homogeneous and homogeneous polynomials, allowing to introduce new families of free divisors which do not come from hyperplane arrangements nor as explicit discriminants from singularity theory.
49 citations
TL;DR: In this paper, the authors focus on the ideal theoretic and homological properties of a plane Cremona map by focusing on its homogeneous base ideal (indeterminacy locus).
47 citations
TL;DR: In this article, a rational map defined by homogeneous forms, of the same degree, in the homogeneous coordinate ring of the graph of a variety parameterized by the Rees algebra is studied.
Abstract: Our object of study is a rational map defined by homogeneous forms , of the same degree , in the homogeneous coordinate ring of . Our goal is to relate properties of , of the homogeneous coordinate ring of the variety parameterized by , and of the Rees algebra , the bihomogeneous coordinate ring of the graph of . For a regular map , for instance, we prove that satisfies Serre’s condition , for some , if and only if satisfies and is birational onto its image. Thus, in particular, is birational onto its image if and only if satisfies . Either condition has implications for the shape of the core, namely, is the multiplier ideal of and Conversely, for , either equality for the core implies birationality. In addition, by means of the generalized rows of the syzygy matrix of , we give an explicit method to reduce the nonbirational case to the birational one when .
30 citations
TL;DR: In this paper, it was shown that the Orlik-Terao algebra is graded isomorphic to the special fiber of the ideal $I$ generated by the $(n-1)$-fold products of the members of a central arrangement of size $n$.
Abstract: It is shown that the Orlik-Terao algebra is graded isomorphic to the special fiber of the ideal $I$ generated by the $(n-1)$-fold products of the members of a central arrangement of size $n$. This momentum is carried over to the Rees algebra (blowup) of $I$ and it is shown that this algebra is of fiber-type and Cohen-Macaulay. It follows by a result of Simis-Vasconcelos that the special fiber of $I$ is Cohen-Macaulay, thus giving another proof of a result of Proudfoot-Speyer about the Cohen-Macauleyness of the Orlik-Terao algebra.
25 citations