Zobrazeno 1 - 10
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pro vyhledávání: '"Dimca, A."'
Autor:
Dimca, Alexandru, Pokora, Piotr
We define the type of a plane curve using the sum of the first two exponents arising from the minimal free resolution of its Jacobian algebra. Then we show that this invariant behaves well with respect to the union of curves. The curves of type $0$ a
Externí odkaz:
http://arxiv.org/abs/2410.11479
Autor:
Dimca, Alexandru, Sticlaru, Gabriel
We define the minimal plus-one generated curves and prove a result explaining why they are the closest relatives of the free curves, after the nearly free curves. Then we look at the projective closures of the general and of the special fibers of som
Externí odkaz:
http://arxiv.org/abs/2406.19795
Autor:
Dimca, Alexandru, Sticlaru, Gabriel
In this notes we study complex projective plane curves whose graded module of Jacobian syzygies is generated by its minimal degree component. Examples of such curves include the smooth curves as well as the maximal Tjurina curves. However, this class
Externí odkaz:
http://arxiv.org/abs/2405.06269
Autor:
Dimca, Alexandru
The Castelnuovo-Mumford regularity of the Jacobian algebra and of the graded module of derivations associated to a general curve arrangement in the complex projective plane are studied. The key result is an addition-deletion type result, similar to r
Externí odkaz:
http://arxiv.org/abs/2401.14959
Autor:
Dimca, Alexandru, Sticlaru, Gabriel
G\"unter Ziegler has shown in 1989 that some homological invariants associated with the free resolutions of Jacobian ideals of line arrangements are not determined by combinatorics. His classical example involves hexagons inscribed in conics. Indepen
Externí odkaz:
http://arxiv.org/abs/2312.11928
Autor:
Dimca, Alexandru
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 the mystery of free curves, many tools were developed and many result
Externí odkaz:
http://arxiv.org/abs/2312.07591
In the present article we construct new families of free and nearly free curves starting from a plane cubic curve $C$ and adding some of its hyperosculating conics. We present results that involve nodal cubic curves and the Fermat cubic. In addition,
Externí odkaz:
http://arxiv.org/abs/2311.08913
Autor:
Dimca, Alexandru
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 free line arrangement, then the resulting line arrangement is either free or pl
Externí odkaz:
http://arxiv.org/abs/2310.08972
In the present paper we compute Alexander polynomials for certain classes of conic-line arrangements in the complex projective plane which are related to pencils. We prove two general results for curve arrangements coming from Halphen pencils of inde
Externí odkaz:
http://arxiv.org/abs/2305.01450
Autor:
Dimca, Alexandru, Ilardi, Giovanna
We show first that a generic hypersurface $V$ of degree $d\geq 3$ in the complex projective space $ \mathbb{P}^n$ of dimension $n \geq 3$ has at least one hyperplane section $V \cap H$ containing exactly $n$ ordinary double points, alias $A_1$ singul
Externí odkaz:
http://arxiv.org/abs/2301.06952