Zobrazeno 1 - 10
of 100
pro vyhledávání: '"Beorchia, Valentina"'
Given a ternary homogeneous polynomial, the fixed points of the map from $\mathbb{P}^2$ to itself defined by its gradient are called its eigenpoints. We focus on cubic polynomials, and analyze configurations of eigenpoints that admit one or more alig
Externí odkaz:
http://arxiv.org/abs/2407.16582
The goal of this paper is to establish a new and efficient characterization of quasi-homogeneous isolated singularities of free curves and nearly free curves $C$ in $\mathbb{P}^2$. The criterion will be in terms of the first syzygy matrix associated
Externí odkaz:
http://arxiv.org/abs/2407.05819
Autor:
Beorchia, Valentina
We prove that any planar projective curve of degree $d \ge 4$ and with a smooth Hessian curve $H_f$ is uniquely determined by $H_f$. Taking into account that the Hessian curve is the ramification divisor associated with the polar map, we prove the st
Externí odkaz:
http://arxiv.org/abs/2406.05423
The Jacobian scheme of a reduced, singular projective plane curve is the zero-dimensional scheme, whose homogeneous ideal is generated by the partials of its defining polynomial. The degree of such a scheme is called the global Tjurina number and, if
Externí odkaz:
http://arxiv.org/abs/2303.04665
Autor:
Beorchia, Valentina, Brundu, Michela
The present paper concerns the question of the violation of the r-th inequality for extremal curves in the projective r-space, posed by T. Kato and G. Martens. We show that the answer is negative in many cases. The result is obtained by a detailed an
Externí odkaz:
http://arxiv.org/abs/2205.13318
This note is motivated by the Question 16 of http://cubics.wikidot.com: Which configurations of 15 points in the projective 3-space arise as eigenpoints of a cubic surface? We prove that a general eigenscheme in the projective n-space is the complete
Externí odkaz:
http://arxiv.org/abs/2205.05196
We study schemes of tensor eigenvectors from an algebraic and geometric viewpoint. We characterize determinantal defining equations of such eigenschemes via linear equations in their coefficients, both in the general and in the symmetric case. We giv
Externí odkaz:
http://arxiv.org/abs/2205.04413
We prove that two general ternary forms are simultaneously identifiable only in the classical cases of two quadratic and a cubic and a quadratic form. We translate the problem into the study of a certain linear system on a projective bundle on the pl
Externí odkaz:
http://arxiv.org/abs/2106.13698
Publikováno v:
SIAM Journal on Applied Algebra and Geometry 5, 2021, n. 4, 620-650
We study projective schemes arising from eigenvectors of tensors, called eigenschemes. After some general results, we give a birational description of the variety parametrizing eigenschemes of general ternary symmetric tensors and we compute its dime
Externí odkaz:
http://arxiv.org/abs/2007.12789
In this paper we study the infinitesimal deformations of a trigonal curve that preserve the trigonal series and such that the associate infinitesimal variation of Hodge structure (IVHS) is of rank 1. We show that if the genus g is greater or equal to
Externí odkaz:
http://arxiv.org/abs/1812.09248