ترغب بنشر مسار تعليمي؟ اضغط هنا

On the Hilbert vector of the Jacobian module of a plane curve

97   0   0.0 ( 0 )
 نشر من قبل Armando Cerminara
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We identify several classes of curves $C:f=0$, for which the Hilbert vector of the Jacobian module $N(f)$ can be completely determined, namely the 3-syzygy curves, the maximal Tjurina curves and the nodal curves, having only rational irreducible components. A result due to Hartshorne, on the cohomology of some rank 2 vector bundles on $mathbb{P}^2$, is used to get a sharp lower bound for the initial degree of the Jacobian module $N(f)$, under a semistability condition.



قيم البحث

اقرأ أيضاً

We describe the 0-th Fitting ideal of the Jacobian module of a plane curve in terms of determinants involving the Jacobian syzygies of this curve. This leads to new characterizations of maximal Tjurina curves, that is of non free plane curves, whose global Tjurina number equals an upper bound given by A. du Plessis and C.T.C. Wall.
51 - Roger Dellaca 2015
We establish a form of the Gotzmann representation of the Hilbert polynomial based on rank and generating degrees of a module, which allow for a generalization of Gotzmanns Regularity Theorem. Under an additional assumption on the generating degrees, the Gotzmann regularity bound becomes sharp. An analoguous modification of the Macaulay representation is used along the way, which generalizes the theorems of Macaulay and Green, and Gotzmanns Persistence Theorem.
In a series of papers, Aluffi and Faber computed the degree of the $GL_3$ orbit closure of an arbitrary plane curve. We attempt to generalize this to the equivariant setting by studying how orbits degenerate under some natural specializations, yieldi ng a fairly complete picture in the case of plane quartics.
A real morsification of a real plane curve singularity is a real deformation given by a family of real analytic functions having only real Morse critical points with all saddles on the zero level. We prove the existence of real morsifications for rea l plane curve singularities having arbitrary real local branches and pairs of complex conjugate branches satisfying some conditions. This was known before only in the case of all local branches being real (ACampo, Gusein-Zade). We also discuss a relation between real morsifications and the topology of singularities, extending to arbitrary real morsifications the Balke-Kaenders theorem, which states that the ACampo--Gusein-Zade diagram associated to a morsification uniquely determines the topological type of a singularity.
175 - Fabian Reede , Ziyu Zhang 2021
Let $X$ be a projective K3 surfaces. In two examples where there exists a fine moduli space $M$ of stable vector bundles on $X$, isomorphic to a Hilbert scheme of points, we prove that the universal family $mathcal{E}$ on $Xtimes M$ can be understood as a complete flat family of stable vector bundles on $M$ parametrized by $X$, which identifies $X$ with a smooth connected component of some moduli space of stable sheaves on $M$.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا