ترغب بنشر مسار تعليمي؟ اضغط هنا

Strong full exceptional collections on certain toric varieties with Picard number three via mutations

69   0   0.0 ( 0 )
 نشر من قبل Wahei Hara
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف Wahei Hara




اسأل ChatGPT حول البحث

In this paper, we study derived categories of certain toric varieties with Picard number three that are blowing-up another toric varieties along their torus invariant loci of codimension at most three. We construct strong full exceptional collections by using Orlovs blow-up formula and mutations.

قيم البحث

اقرأ أيضاً

We study instanton bundles $E$ on $mathbb{P}^1times mathbb{P}^1 times mathbb{P}^1$. We construct two different monads which are the analog of the monads for instanton bundles on $mathbb P^3$ and on the flag threefold $F(0,1,2)$. We characterize the G ieseker semistable cases and we prove the existence of $mu$-stable instanton bundles generically trivial on the lines for any possible $c_2(E)$. We also study the locus of jumping lines.
We develop an analogue of Eisenbud-Floystad-Schreyers Tate resolutions for toric varieties. Our construction, which is given by a noncommutative analogue of a Fourier-Mukai transform, works quite generally and provides a new perspective on the relati onship between Tate resolutions and Beilinsons resolution of the diagonal. We also develop a Beilinson-type resolution of the diagonal for toric varieties and use it to generalize Eisenbud-Floystad-Schreyers computationally effective construction of Beilinson monads.
We call a sheaf on an algebraic variety immaculate if it lacks any cohomology including the zero-th one, that is, if the derived version of the global section functor vanishes. Such sheaves are the basic tools when building exceptional sequences, inv estigating the diagonal property, or the toric Frobenius morphism. In the present paper we focus on line bundles on toric varieties. First, we present a possibility of understanding their cohomology in terms of their (generalized) momentum polytopes. Then we present a method to exhibit the entire locus of immaculate divisors within the class group. This will be applied to the cases of smooth toric varieties of Picard rank two and three and to those being given by splitting fans. The locus of immaculate line bundles contains several linear strata of varying dimensions. We introduce a notion of relative immaculacy with respect to certain contraction morphisms. This notion will be stronger than plain immaculacy and provides an explanation of some of these linear strata.
We study the proalgebraic space which is the inverse limit of all finite branched covers over a normal toric variety $X$ with branching set the invariant divisor under the action of $(mathbb{C}^*)^n$. This is the proalgebraic toric-completion $X_{mat hbb{Q}}$ of $X$. The ramification over the invariant divisor and the singular invariant divisors of $X$ impose topological constraints on the automorphisms of $X_{mathbb{Q}}$. Considering this proalgebraic space as the toric functor on the adelic complex plane multiplicative semigroup, we calculate its automorphic group. Moreover we show that its vector bundle category is the direct limit of the respective categories of the finite toric varieties coverings defining the proalgebraic toric-completion.
We give a characterization of all complete smooth toric varieties whose rational homotopy is of elliptic type. All such toric varieties of complex dimension not more than three are explicitly described.
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