ترغب بنشر مسار تعليمي؟ اضغط هنا

A supplement to Fujinos paper: On isolated log canonical singularities with index one

246   0   0.0 ( 0 )
 نشر من قبل Shihoko Ishii
 تاريخ النشر 2013
  مجال البحث
والبحث باللغة English
 تأليف Shihoko Ishii




اسأل ChatGPT حول البحث

Let $E$ be the essential part of the exceptional locus of a good resolution of an isolated, log canonical singularity of index one. We describe the dimension of the dual complex of $E$ in terms of the Hodge type of $H^{n-1}(E, O_E)$, which is one of the main results of the paper [1] of Fujino. Our proof uses only an elementary classical method, while Fujinos argument depends on the recent development in minimal model theory.



قيم البحث

اقرأ أيضاً

We study foliations $mathcal{F}$ on Hirzebruch surfaces $S_delta$ and prove that, similarly to those on the projective plane, any $mathcal{F}$ can be represented by a bi-homogeneous polynomial affine $1$-form. In case $mathcal{F}$ has isolated singul arities, we show that, for $ delta=1 $, the singular scheme of $mathcal{F}$ does determine the foliation, with some exceptions that we describe, as is the case of foliations in the projective plane. For $delta eq 1$, we prove that the singular scheme of $mathcal{F}$ does not determine the foliation. However we prove that, in most cases, two foliations $mathcal{F}$ and $mathcal{F}$ given by sections $s$ and $s$ have the same singular scheme if and only if $s=Phi(s)$, for some global endomorphism $Phi $ of the tangent bundle of $S_delta$.
109 - Osamu Fujino 2020
We establish a relative spannedness for log canonical pairs, which is a generalization of the basepoint-freeness for varieties with log-terminal singularities by Andreatta--Wisniewski. Moreover, we establish a generalization for quasi-log canonical pairs.
A conic bundle is a contraction $Xto Z$ between normal varieties of relative dimension $1$ such that $-K_X$ is relatively ample. We prove a conjecture of Shokurov which predicts that, if $Xto Z$ is a conic bundle such that $X$ has canonical singulari ties and $Z$ is $mathbb{Q}$-Gorenstein, then $Z$ is always $frac{1}{2}$-lc, and the multiplicities of the fibers over codimension $1$ points are bounded from above by $2$. Both values $frac{1}{2}$ and $2$ are sharp. This is achieved by solving a more general conjecture of Shokurov on singularities of bases of lc-trivial fibrations of relative dimension $1$ with canonical singularities.
By the fundamental work of Griffiths one knows that, under suitable assumption, homological and algebraic equivalence do not coincide for a general hypersurface section of a smooth projective variety $Y$. In the present paper we prove the same result in case $Y$ has isolated singularities.
159 - Noemie Combe 2014
The decomposition of a two dimensional complex germ with non-isolated singularity into semi-algebraic sets is given. This decomposition consists of four classes: Riemannian cones defined over a Seifert fibered manifold, a topological cone over thicke ned tori endowed with Cheeger-Nagase metric, a topological cone over mapping torus endowed with Hsiang-Pati metric and a topological cone over the tubular neighbourhoods of the links singularities. In this decomposition there exist semi-algebraic sets that are metrically conical over the manifolds constituting the link. The germ is reconstituted up to bi-Lipschitz equivalence to a model describing its geometric behavior.
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