相关论文: Pseudoconvexity at infinity in Hodge theory: a cod…

We construct projective toroidal compactifications for integral models of Shimura varieties of Hodge type. We also construct integral models of the minimal (Satake-Baily-Borel) compactification. Our results essentially reduce the problem to…

We consider a filtration on the cohomology of the structure sheaf indexed by (not necessarily reduced) divisors ``at infinity''. We show that the filtered pieces have transfers morphisms, fpqc descent, and are so called cube invariant. In…

In the spirit of Kobayashi's applications of methods of invariant metrics to questions of projective geometry, we introduce a projective analogue of the complex squeezing function. Using Frankel's work, we prove that for convex domains it…

In this note, we derive a uniqueness theorem for minimal graphs of general codimension under certain restrictions closed related to the convexity (not strict convexity) of the area functional with respect to singular values, improving the…

In this paper we give different compactifications for the domain and the codomain of an affine rational map $f$ which parametrizes a hypersurface. We show that the closure of the image of this map (with possibly some other extra…

We investigate properties of the Hodge metric of a mixed period domain. In particular, we calculate its curvature and the curvature of the Hodge bundles. We also consider when the pull back metric via a period map is K\"ahler. Several…

We investigate the possibility of extension of $F_\sigma$-measurable and Baire-one maps from subspaces of topological spaces when these maps take values in spaces which covers by a sequence of metrizable spaces with special properties

For a two dimensional bounded pseudoconvex domain of finite type, we prove uniformization theorems via K$\ddot{\operatorname{a}}$hler-Kobayashi metric or K$\ddot{\operatorname{a}}$hler-Carath$\acute{\operatorname{e}}$odory metric with…

We present a generalization of the notion of neighborliness to non-polyhedral convex cones. Although a definition of neighborliness is available in the non-polyhedral case in the literature, it is fairly restrictive as it requires all the…

With the goal of obtaining strong relaxations for binary polynomial optimization problems, we introduce the pseudo-Boolean polytope defined as the convex hull of the set of binary points satisfying a collection of equations containing…

We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…

H-holomorphic maps are a parameter version of J-holomorphic maps into contact manifolds. They have arisen in efforts to prove the existence of higher--genus holomorphic open book decompositions and efforts to prove the existence of finite…

We address a number of problems concerning the (im)possibility of either extending locally trivial subbundles of possibly singular Banach/$C^*$ bundles globally, embedding subhomogeneous bundles into homogeneous ones, or recovering locally…

We present a range of applications of localisation for constrained transports for pairs of probability measures in order with respect to a lattice cone. These examples comprise irreducible convex paving for martingale transports in…

We develop a framework that systematically casts the solvability and uniqueness conditions of linearized geometric boundary-value problems into cohomological terms. The theory is designed to be applicable without assumptions on the…

In this work we describe horofunction compactifications of metric spaces and finite dimensional real vector spaces through asymmetric metrics and asymmetric polyhedral norms by means of nonstandard methods, that is, ultrapowers of the…

We provide new conditions under which the alternating projection sequence converges in norm for the convex feasibility problem where a linear subspace with finite codimension $N\geq 2$ and a lattice cone in a Hilbert space are considered.…

In this paper we answer positively a question raised by Kapovich and Leeb in a paper titled "Finsler bordifications of symmetric and certain locally symmetric spaces". Specifically, we show that for a finite-dimensional vector space with a…

A closure system with the anti-exchange axiom is called a convex geometry. One geometry is called a sub-geometry of the other if its closed sets form a sublattice in the lattice of closed sets of the other. We prove that convex geometries…

Our objective in this article is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of the (say) simplicial set embedded in a finite dimensional vector space…