ترغب بنشر مسار تعليمي؟ اضغط هنا

Polyvector fields for Fano 3-folds

80   0   0.0 ( 0 )
 نشر من قبل Fabio Tanturri
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We compute the Hochschild-Kostant-Rosenberg decomposition of the Hochschild cohomology of Fano 3-folds. This is the first step in understanding the non-trivial Gerstenhaber algebra structure, and yields some initial insights in the classification of Poisson structures on Fano 3-folds of higher Picard rank.



قيم البحث

اقرأ أيضاً

This paper studies the defect of terminal Gorenstein Fano 3 folds. I determine a bound on the defect of terminal Gorenstein Fano 3-folds of Picard rank 1 that do not contain a plane. I give a general bound for quartic 3-folds and indicate how to stud y the defect of terminal Gorenstein Fano 3-folds with Picard rank 1 that contain a plane.
We prove a Bogomolov-Gieseker type inequality for the third Chern characters of stable sheaves on Calabi-Yau 3-folds and a large class of Fano 3-folds with given rank and first and second Chern classes. The proof uses the spreading-out technique, van ishings from the tilt-stability conditions, and Langers estimation theorem of the global sections of torsion free sheaves. In particular, the result implies that the conjectural sufficient conditions on the Chern numbers for the existence of stable sheaves on a Calabi-Yau 3-fold by Douglas-Reinbacher-Yau needs to be modified.
We construct some new deformation families of four-dimensional Fano manifolds of index $1$ in some known classes of Gorenstein formats. These families have explicit descriptions in terms of equations, defining their image under the anti-canonical emb edding in some weighted projective space. The constructed families have relatively smaller anti-canonical degrees than most other known families of smooth Fano 4-folds.
Let $Xsubset mathbb{P}^4$ be a terminal factorial quartic $3$-fold. If $X$ is non-singular, $X$ is emph{birationally rigid}, i.e. the classical MMP on any terminal $mathbb{Q}$-factorial projective variety $Z$ birational to $X$ always terminates with $X$. This no longer holds when $X$ is singular, but very few examples of non-rigid factorial quartics are known. In this article, we first bound the local analytic type of singularities that may occur on a terminal factorial quartic hypersurface $Xsubset mathbb{P}^4$. A singular point on such a hypersurface is either of type $cA_n$ ($ngeq 1$), or of type $cD_m$ ($mgeq 4$), or of type $cE_6, cE_7$ or $cE_8$. We first show that if $(P in X)$ is of type $cA_n$, $n$ is at most $7$, and if $(P in X)$ is of type $cD_m$, $m$ is at most $8$. We then construct examples of non-rigid factorial quartic hypersurfaces whose singular loci consist (a) of a single point of type $cA_n$ for $2leq nleq 7$ (b) of a single point of type $cD_m$ for $m= 4$ or $5$ and (c) of a single point of type $cE_k$ for $k=6,7$ or $8$.
512 - Jungkai A. Chen , Meng Chen 2013
We prove the Conjecture of Catenese--Chen--Zhang: the inequality $K_X^3geq frac{4}{3}p_g(X)-frac{10}{3}$ holds for all projective Gorenstein minimal 3-folds $X$ of general type.
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