ترغب بنشر مسار تعليمي؟ اضغط هنا

Classification of toric manifolds over an $n$-cube with one vertex cut

220   0   0.0 ( 0 )
 نشر من قبل Seonjeong Park
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We say that a complete nonsingular toric variety (called a toric manifold in this paper) is over $P$ if its quotient by the compact torus is homeomorphic to $P$ as a manifold with corners. Bott manifolds (or Bott towers) are toric manifolds over an $n$-cube $I^n$ and blowing them up at a fixed point produces toric manifolds over $mathrm{vc}(I^n)$ an $n$-cube with one vertex cut. They are all projective. On the other hand, Odas $3$-fold, the simplest non-projective toric manifold, is over $mathrm{vc}(I^n)$. In this paper, we classify toric manifolds over $mathrm{vc}(I^n)$ $(nge 3)$ as varieties and also as smooth manifolds. As a consequence, it turns out that (1) there are many non-projective toric manifolds over $mathrm{vc}(I^n)$ but they are all diffeomorphic, and (2) toric manifolds over $mathrm{vc}(I^n)$ in some class are determined by their cohomology rings as varieties among toric manifolds.



قيم البحث

اقرأ أيضاً

401 - Sho Hasui 2013
A quasitoric manifold is a smooth manifold with a locally standard torus action for which the orbit space is identified with a simple polytope. For a class of topological spaces, the class is called strongly cohomologically rigid if any isomorphism o f cohomology rings can be realized as a homeomorphism. This paper shows the strong cohomological rigidity of the class of quasitoric manifolds over $I^3$.
In the present paper, we characterize Fano Bott manifolds up to diffeomorphism in terms of three operations on matrix. More precisely, we prove that given two Fano Bott manifolds $X$ and $X$, the following conditions are equivalent: (1) the upper tri angular matrix associated to $X$ can be transformed into that of $X$ by those three operations; (2) $X$ and $X$ are diffeomorphic; (3) the integral cohomology rings of $X$ and $X$ are isomorphic as graded rings. As a consequence, we affirmatively answer the cohomological rigidity problem for Fano Bott manifolds.
260 - Sho Hasui 2014
The aim of this article is to establish the notion of bundle-type quasitoric manifolds and provide two classification results on them: (1) ($mathbb{C}P^2sharpmathbb{C}P^2$)-bundle type quasitoric manifolds are weakly equivariantly homeomorphic if the ir cohomology rings are isomorphic, and (2) quasitoric manifolds over $I^3$ are homeomorphic if their cohomology rings are isomorphic. In the latter case, there are only four quasitoric manifolds up to weakly equivariant homeomorphism which are not bundle-type.
We establish upper bounds of the indices of topological Brauer classes over a closed orientable 8-manifolds. In particular, we verify the Topological Period-Index Conjecture (TPIC) for topological Brauer classes over closed orientable 8-manifolds of order not congruent to 2 mod 4. In addition, we provide a counter-example which shows that the TPIC fails in general for closed orientable 8-manifolds.
244 - Sho Hasui 2013
For a simple $n$-polytope $P$, a quasitoric manifold over $P$ is a $2n$-dimensional smooth manifold with a locally standard action of the $n$-dimensional torus for which the orbit space is identified with $P$. This paper shows the topological classif ication of quasitoric manifolds over the dual cyclic polytope $C^n(m)^*$, when $n>3$ or $m-n=3$. Besides, we classify small covers, the real version of quasitoric manifolds, over all dual cyclic polytopes.
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