For any degenerating Calabi–Yau family, we introduce a new limit space which call galaxy, whose dense subspace is the disjoint union of countably infinite open varieties, parametrized by rational points Kontsevich–Soibelman’s essential skeleton, while dominated Huber adification over Puiseux series field. Other topics include: projective limits toroidal compactifications (Sect. 3), locally mode...

This paper presents cone compression and expansion fixed point results of KrasnoselskiiPetryshyn type formultimaps between Fréchet spaces. Two approaches have recently been presented in the literature, both of which are based on the fact that a Fréchet space can be viewed as a projective limit of a sequence of Banach spaces {En}n∈N (here N= {1,2, . . .}). Both approaches are based on constructi...

In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.

We construct covariant q-deformed holomorphic structures for all finitely generated relative Hopf modules over the irreducible quantum flag manifolds endowed with their Heckenberger–Kolb calculi. In classical limit, these reduce to of sections homogeneous vector bundles manifolds. For case simple modules, we show that this structure is unique. This generalises earlier work Majid, Khalkhali, Lan...

We study the prime-to-p Hecke action on projective limit of sets connected components Shimura varieties with fixed parahoric or Bruhat–Tits level at p. In particular, we construct infinitely many for CM unitary groups in odd variables which considered actions are not transitive. prove this result by giving negative examples question Bruhat–Colliot-Thélène–Sansuc–Tits and its variant, related to...

The tangent bundle of a wide class of Fréchet manifolds is studied here. A vector bundle structure is obtained with structural group a topological subgroup of the general linear group of the fiber type. Moreover, basic geometric results, known form the classical case of finite dimensional manifolds, are recovered here: Connections can be defined and are characterized by a generalized type of Ch...

We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple, explicit method, such as a spatial centered flux/forward Euler time integration, and subsequently projects the results forward in time over a large time step on ...

Let V + = ⊕i∈IO(ki) and V − = ⊕j∈JO(−lj) be vector bundles on P s with ki and lj positive integers. Suppose X ι →֒ Ps is the zero locus of a generic section of V + and Y is a projective manifold such that X j →֒ Y with normal bundle NX/Y = ι ∗(V −). The relations between Gromov-Witten theories of X and Y are studied here by means of a suitably defined equivariant Gromov-Witten theory in Ps. We ap...

For a smooth projective variety whose anti-canonical bundle is nef, we prove confluence of the small K -theoretic J -function, i.e., after rescaling appropriately Novikov variables, -function has limit when q → 1 , which coincides with cohomological -function. Furthermore, in case Fano toric manifold Picard rank 2, version an identity due to Iritani that compares I and oscillatory integral mirr...