اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدUlrich Bundles on Cubic Fourfolds
120
0
0.0
(
0
)
تأليف
Daniele Faenzi
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf E of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an E appears as an extension of two Lehn-Lehn-Sorger-van Straten sheaves. Then we prove that a general deformation of E(1) becomes Ulrich. In particular, this says that general cubic fourfolds have Ulrich complexity 6.
قيم البحث
اقرأ أيضاً
We show that any polarized K3 surface supports special Ulrich bundles of rank 2.
We assume that $mathcal{E}$ is a rank $r$ Ulrich bundle for $(P^n, mathcal{O}(d))$. The main result of this paper is that $mathcal{E}(i)otimes Omega^{j}(j)$ has natural cohomology for any integers $i in mathbb{Z}$ and $0 leq j leq n$, and every Ulric
h bundle $mathcal{E}$ has a resolution in terms of $n$ of the trivial bundle over $P^n$. As a corollary, we can give a necessary and sufficient condition for Ulrich bundles if $n leq 3$, which can be used to find some new examples, i.e., rank $2$ bundles for $(P^3, mathcal{O}(2))$ and rank $3$ bundles for $(P^2, mathcal{O}(3))$.
We show that the maximal number of planes in a complex smooth cubic fourfold in ${mathbb P}^5$ is $405$, realized by the Fermat cubic only; the maximal number of real planes in a real smooth cubic fourfold is $357$, realized by the so-called Clebsch-
-Segre cubic. Altogether, there are but three (up to projective equivalence) cubics with more than $350$ planes.
In [1309.1899], Ranestad and Voisin showed, quite surprisingly, that the divisor in the moduli space of cubic fourfolds consisting of cubics apolar to a Veronese surface is not a Noether-Lefschetz divisor. We give an independent proof of this by exhi
biting an explicit cubic fourfold X in the divisor and using point counting methods over finite fields to show X is Noether-Lefschetz general. We also show that two other divisors considered in [ibid.] are not Noether-Lefschetz divisors.
We classify the Ulrich vector bundles of arbitrary rank on smooth projective varieties of minimal degree. In the process, we prove the stability of the sheaves of relative differentials on rational scrolls.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
