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Hodge sheaves underlying flat projective families
We show that, for any fixed weight, there is a natural system of Hodge sheaves, whose Higgs field has no poles, arising from a flat projective family...
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Families of Singular Chern–Ricci Flat Metrics
We prove uniform a priori estimates for degenerate complex Monge–Ampère equations on a family of hermitian varieties. This generalizes a theorem of...
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On algebraic Chern classes of flat vector bundles
We show that under some assumptions on the monodromy group some combinations of higher Chern classes of a flat vector bundle are torsion in the Chow...
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On Equicontinuity of the Families of Map**s with One Normalization Condition in Terms of Prime Ends
We study map**s with branching satisfying certain conditions of distortion for the modulus of families of paths. Under the conditions that the...
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Kähler Geometry of Scalar Flat Metrics on Line Bundles Over Polarized Kähler–Einstein Manifolds
In view of a better understanding of the geometry of scalar flat Kähler metrics, this paper studies two families of scalar flat Kähler metrics...
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Birational geometry of smooth families of varieties admitting good minimal models
We study families of projective manifolds with good minimal models. After constructing a suitable moduli functor for polarized varieties with...
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On Abel–Jacobi maps of Lagrangian families
We study in this article the cohomological properties of Lagrangian families on projective hyper-Kähler manifolds. First, we give a criterion for the...
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Flat Mittag-Leffler Modules, and Their Relative and Restricted Versions
Assume that R is a non-right perfect ring. Then there is a proper class of classes of (right R-) modules closed under transfinite extensions lying...
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Quantitative equidistribution and the local statistics of the spectrum of a flat torus
We show that a pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with...
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Isoparametric families of submanifolds
In this paper we present a generalization of the theory of isoparametric families of hypersurfaces in a Riemannian manifold of constant curvature, in...
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Singularities of Flat Dual Surfaces of Cuspidal Edges in the Three-Sphere from Duality Viewpoint
We focus on investigating the differential geometric properties of cuspidal edge in the three-sphere from a viewpoint of duality. Using Legendrian...
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The generalized Pythagorean theorem on the compactifications of certain dually flat spaces via toric geometry
In this paper we study dually flat spaces arising from Delzant polytopes equipped with a symplectic potential together with their corresponding toric...
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Zero-cycles in families of rationally connected varieties
We study zero-cycles in families of rationally connected varieties. We show that for a smooth projective scheme over a henselian discrete valuation...
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On the distribution of Alexander polynomials in certain families of closed braids
We study the distribution of arithmetic invariants associated to Alexander polynomials for certain infinite families of links. The families of links...
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Sizes of Flat Maximal Antichains of Subsets
This is the second of two papers investigating for which positive integers m there exists a maximal antichain of size m in the Boolean lattice
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Minimal Rational Curves and 1-Flat Irreducible G-Structures
1-Flat irreducible G-structures, equivalently, irreducible G-structures admitting torsion-free affine connections, have been studied extensively in...
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A formal model of Coleman families and applications to Iwasawa invariants
For a given Coleman family of modular forms, we construct a formal model and prove the existence of a family of Galois representations associated to...
