Related papers: Some conjectures on continuous rational maps into …

In this follow-up of our earlier two works D(11.1) (arXiv:1406.0929 [math.DG]) and D(11.2) (arXiv:1412.0771 [hep-th]) in the D-project, we study further the notion of a `differentiable map from an Azumaya/matrix manifold to a real…

The present paper mainly presents, for example, explicit classifications of compact smooth manifolds having non-empty boundaries and simple structures where the dimensions are general. Studies of this type is fundamental and important. They…

We study the dynamics of algebraic families of maps on $\mathbb{P}^N$, over the field $\mathbb{C}$ of complex numbers, and the geometry of their preperiodic points. The goal of this note is to formulate a conjectural characterization of the…

We study the geometry of the space of rational curves on smooth complete intersections of low degree, which pass through a given set of points on the variety. The argument uses spreading out to a finite field, together with an adaptation to…

We introduce the notion of families of n-marked smooth rational tropical curves over smooth tropical varieties and establish a one-to-one correspondence between (equivalence classes of) these families and morphisms from smooth tropical…

As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…

We show that manifolds admitting special generic maps also admit nice generalized multisections. Special generic maps are natural generalized versions of Morse functions with exactly two singular points on closed manifolds, characterizing…

In the relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture, we formulate a local conjecture (arithmetic transfer) in the case of an exotic smooth formal moduli space of p-divisible groups, associated to a unitary…

We continue the work started in part I (q-alg/9706004) and prove the invariance and universality in the class of finite type invariants of the object defined and motivated there, namely the Aarhus integral of rational homology 3-spheres.…

We prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs.…

We consider rationally connected complex projective manifolds M and show that their loop spaces--infinite dimensional complex manifolds--have properties similar to those of M. Furthermore, we give a finite dimensional application concerning…

Fold maps are fundamental tools in the theory of singularities of differentiable maps and its applications to geometry. They are higher dimensional variants of Morse functions. Classes of special generic maps and round fold maps are…

Let X be a smooth algebraic variety on which a solvable Lie group acts freely on a dense open orbit. Such varieties include generalized flag varieties, toric varieties, Bott-Samelson varieties, and many spherical varieties, as well as…

We define a graph algebra version of the stationary phase integration over the coadjoint orbits in the Reshetikhin formula for the colored Jones-HOMFLY polynomial. As a result, we obtain a `universal' U(1)-RCC invariant of links in rational…

Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f: O -> P between smooth orbifolds O and P. We show that Sard's theorem holds and that the inverse image of a regular value is a…

We study the moduli space of $J$-holomorphic subvarieties in a $4$-dimensional symplectic manifold. For an arbitrary tamed almost complex structure, we show that the moduli space of a sphere class is formed by a family of linear system…

In this note, we give a brief survey on some recent developments of biharmonic submanifolds. After reviewing some recent progress on Chen's biharmonic conjecture, the Generalized Chen's conjecture on biharmonic submanifolds of…

For a dominant rational self-map on a smooth projective variety defined over a number field, Kawaguchi and Silverman conjectured that the (first) dynamical degree is equal to the arithmetic degree at a rational point whose forward orbit is…

We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of…

One of the most powerful ideas in the study and classification of algebraic varieties is the notion of a model: that is, to single out an object, in the appropriate isomorphism class, with nice properties. This survey aims to define and…