Free and nearly free curves vs. rational cuspidal plane curves
A Dimca, G Sticlaru - Publications of the Research Institute for …, 2018 - ems.press
Free and Nearly Free Curves vs. Rational Cuspidal Plane Curves Page 1 Publ. RIMS Kyoto
Univ. 54 (2018), 163–179 DOI 10.4171/PRIMS/54-1-6 Free and Nearly Free Curves vs …
Univ. 54 (2018), 163–179 DOI 10.4171/PRIMS/54-1-6 Free and Nearly Free Curves vs …
On free curves and related open problems
A Dimca - arXiv preprint arXiv:2312.07591, 2023 - arxiv.org
In this paper we collect the main properties of free curves in the complex projective plane
and a lot of conjectures and open problems, both old and new. In the quest to understand …
and a lot of conjectures and open problems, both old and new. In the quest to understand …
Maximizing curves viewed as free curves
The aim of this paper is to provide a direct link between maximizing curves that occur in the
construction of smooth algebraic surfaces having the maximal possible Picard numbers and …
construction of smooth algebraic surfaces having the maximal possible Picard numbers and …
On free and plus-one generated curves arising from free curves by addition-deletion of a line
A Dimca - arXiv preprint arXiv:2310.08972, 2023 - arxiv.org
In a recent paper, after introducing the notion of plus-one generated hyperplane
arrangements, Takuro Abe has shown that if we add (resp. delete) a line to (resp. from) a …
arrangements, Takuro Abe has shown that if we add (resp. delete) a line to (resp. from) a …
Conic-line arrangements in the complex projective plane
P Pokora, T Szemberg - Discrete & Computational Geometry, 2023 - Springer
The main goal of this note is to begin a systematic study on conic-line arrangements in the
complex projective plane. We show a de Bruijn–Erdős type inequality and Hirzebruch-type …
complex projective plane. We show a de Bruijn–Erdős type inequality and Hirzebruch-type …
Plane curves with three syzygies, minimal Tjurina curves, and nearly cuspidal curves
A Dimca, G Sticlaru - Geometriae Dedicata, 2020 - Springer
We start the study of reduced complex projective plane curves, whose Jacobian syzygy
module has 3 generators. Among these curves one finds the nearly free curves introduced …
module has 3 generators. Among these curves one finds the nearly free curves introduced …
Free divisors and rational cuspidal plane curves
A Dimca, G Sticlaru - arXiv preprint arXiv:1504.01242, 2015 - arxiv.org
arXiv:1504.01242v4 [math.AG] 1 May 2015 Page 1 arXiv:1504.01242v4 [math.AG] 1 May
2015 FREE DIVISORS AND RATIONAL CUSPIDAL PLANE CURVES ALEXANDRU DIMCA1 …
2015 FREE DIVISORS AND RATIONAL CUSPIDAL PLANE CURVES ALEXANDRU DIMCA1 …
On the exponents of free and nearly free projective plane curves
A Dimca, G Sticlaru - Revista matemática complutense, 2017 - Springer
We show that all the possible pairs of integers occur as exponents for free or nearly free
irreducible plane curves and line arrangements, by producing only two types of simple …
irreducible plane curves and line arrangements, by producing only two types of simple …
On rational cuspidal plane curves and the local cohomology of Jacobian rings
A Dimca - Commentarii Mathematici Helvetici, 2019 - ems.press
This note gives the complete projective classification of rational, cuspidal plane curves of
degree at least 6, and having only weighted homogeneous singularities. It also sheds new …
degree at least 6, and having only weighted homogeneous singularities. It also sheds new …
On the freeness of rational cuspidal plane curves
A Dimca, G Sticlaru - arXiv preprint arXiv:1802.06688, 2018 - arxiv.org
We bring additional support to the conjecture saying that a rational cuspidal plane curve is
either free or nearly free. This conjecture was confirmed for curves of even degree, and in …
either free or nearly free. This conjecture was confirmed for curves of even degree, and in …