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The main result is a wall crossing formula for central projections defined on submanifolds of a real projective space. Our formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the…
We discuss discrete Morrey spaces and their generalizations, and we prove necessary and sufficient conditions for the inclusion property among these spaces through an estimate for the characteristic sequences.
We determine those maps between affine or projective spaces that are linear in the abstract sense of transforming collinear points into collinear points and whose restriction to any line is constant or injective. Our results are extensions…
We present a framework for characterizing injectivity of classes of maps (on cosets of a linear subspace) by injectivity of classes of matrices. Using our formalism, we characterize injectivity of several classes of maps, including…
We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed $\mathrm{PGL}_2(\mathbb{C})$ local systems on the…
Based on the fact that projective monomial curves in the plane are complete intersections, we give an effective inductive method for creating infinitely many monomial curves in the projective $n$-space that are set theoretic complete…
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…
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 classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to this problem and a certain type of minimal…
Assuming Hartshorne's conjecture on complete intersections, we classify projective bundles over projective spaces which has a smooth blow up structure over another projective space. Under some assumptions, we also classify projective…
A new construction of naturally reductive spaces is presented. This construction gives a large amount of new families of naturally reductive spaces. First the infinitesimal models of the new naturally reductive spaces are constructed. A…
The purpose of this article is to study the uniqueness problem for meromorphic mappings from $\mathbb{C}^{n}$ into the complex projective space $\mathbb{P}^{N}(\mathbb{C}).$ By making using of the method of dealing with multiple values due…
We develop a theory of conically smooth stratified spaces and their smooth moduli, including a notion of classifying maps for tangential structures. We characterize continuous space-valued sheaves on these conically smooth stratified spaces…
We show that the spaces of holomorphic and continuous maps from a smooth complex projective variety to a projective space have the same homology in a range depending on the degree of the maps.
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.
A theorem of Jannsen asserts that if a smooth projective variety has injective cycle class maps, it has surjective cycle class maps. The object of this note is to present a version of Jannsen's theorem for singular quasi--projective…
We construct an injective map from the set of holomorphic equivalence classes of neighborhoods $M$ of a compact complex manifold $C$ into ${\mathbb C}^m$ for some $m<\infty$ when $(TM)|_C$ is fixed and the normal bundle of $C$ in $M$ is…
We study the number of planes for four dimensional projective hypersurfaces which has so-called inductive structure. We also determine transcendental lattices for cubic fourfolds of this type.
We introduce the notion of order projections using the order unit property of a positive element in an order unit space and characterize them in terms of (geometric) orthogonality. We describe order projections of the order unit space…