arXiv subjects

Nguyen Thi Ngoc Giao

Publications and source records attributed to Nguyen Thi Ngoc Giao.

4 recordsLinked to original sources

arXiv2026

On plane Cremona maps of degree 4 and length 2

Plane Cremona maps of degree four are divided into two different classes according to their homaloidal type: either they are de Jonquières, that is, they have a base point of multiplicity 3, or they are not de Jonquières. The maps of the former class have length one, while the maps of the latter class have length two, according to the definition of length of a plane Cremona map given by Blanc and Furter. In this paper, we classify plane Cremona maps of degree four and length two, up to the action of automorphisms of the projective plane on the left-hand side and on the right-hand side of the map. This classification also allows us to compute the ordinary quadratic length of all such maps. In particular, we show that this ordinary quadratic length is at most 7 and we classify those maps which attain this upper bound.

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arXiv2026

On the quadratic length of plane Cremona maps of degree 4

Every non-linear plane Cremona map can be decomposed into quadratic maps, and the minimum number of quadratic maps required is called its quadratic length. It is known that plane Cremona maps of degree 3 have quadratic length either 2 or 3. In this paper, we study the quadratic length of plane Cremona maps $φ$ of degree 4. Recall that either $φ$ is de Jonquières, i.e. it has a base point of multiplicity 3, or it is not de Jonquières. In the latter case, $φ$ has quadratic length 2, whereas in the former case we prove that $φ$ has quadratic length 3, 4, or 5, and we classify those maps that reach the upper bound.

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arXiv2023

Newton polytope of good symmetric polynomials

We introduce a general class of symmetric polynomials that have saturated Newton polytope and their Newton polytope has integer decomposition property. The class covers numerous previously studied symmetric polynomials.

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arXiv2022

A characterization of the algebraic degree in semidefinite programming

In this article, we show that the algebraic degree in semidefinite programming can be expressed in terms of the coefficient of a certain monomial in a doubly symmetric polynomial. This characterization of the algebraic degree allows us to use the theory of symmetric polynomials to obtain many interesting results of Nie, Ranestad and Sturmfels in a simpler way.

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