A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The purpose of this article is to develop techniques for estimating basis log canonical thresholds on logarithmic surfaces. To that end, we develop new local intersection estimates that imply log canonicity. Our main motivation and application is to show the existence of Kahler-Einstein edge metrics on all but finitely…
The paper studies foliations on smooth projective varieties and their properties.
problem Characterizing and understanding foliations on smooth projective varieties.
method Develops a structure theorem for smooth projective varieties with almost nef regular foliations, using a smooth morphism and MRC fibration.
result An almost nef regular foliation on a smooth projective variety can be decomposed into a numerically flat regular foliation and a smooth morphism.
Let X be a normal complex projective variety with at worst klt singularities, and L a big line bundle on X. We use valuations to study the log canonical threshold of L, as well as another invariant, the stability threshold. The latter generalizes a notion by Fujita and Odaka, and can be used to characterize when a Q-Fa…
We propose a statistical approach to tornadoes modeling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modeling the tornadoes intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornadoes …
For any Q-Gorenstein klt singularity (X,o), we introduce a normalized volume function vol that is defined on the space of real valuations centered at o and consider the problem of minimizing vol. We prove that the normalized volume has a uniform positive lower bound by pro…
New approach finds analytic interpretation of algebraic invariants for balanced metrics.
problem Finding analytic interpretation of algebraic invariants for balanced metrics.
method Using log canonical thresholds and basis divisors, the approach involves quantized Ding functionals on Bergman spaces.
result Each δ_m is the coercivity threshold of a quantized Ding functional on the m-th Bergman space, characterizing the existence of balanced metrics.
We show that the anti-canonical volume of an n-dimensional Kähler-Einstein Q-Fano variety is bounded from above by certain invariants of the local singularities, namely lctn⋅mult for ideals and the normalized volume function for real valuations. This refines a recent result by Fuji…
The paper establishes inequalities for Chern classes and Riemann-Roch type inequalities for projective manifolds.
problem Establishing inequalities for Chern classes and Riemann-Roch type inequalities for projective manifolds.
method Applying effective very ampleness of adjoint bundles, log-concavity, and Khovanskii-Teissier inequalities.
result For any projective manifold X and ample line bundle L, there exists a universal bivariate polynomial Q_λ(x, y) with deg Q ≤ d, such that the inequality holds.
We first notice in this article that if a compact Kähler manifold has the same integral cohomology ring and Pontrjagin classes as the complex projective space CPn, then it is biholomorphic to CPn provided n is odd. The same holds for even n if we further assume that M is simply-connected. …
We are concerned in this article with a classical question in spectral geometry dating back to McKean-Singer, Patodi and Tanno: whether or not the constancy of holomorphic sectional curvature of a complex n-dimensional compact Kähler manifold can be completely determined by the eigenvalues of its p-Laplacian for a …
We present a model for random simple graphs with a degree distribution that obeys a power law (i.e., is heavy-tailed). To attain this behavior, the edge probabilities in the graph are constructed from Bertoin-Fujita-Roynette-Yor (BFRY) random variables, which have been recently utilized in Bayesian statistics for the c…
Let L be a holomorphic line bundle over a compact complex projective Hermitian manifold X. Any fixed smooth hermitian metric h on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k th tensor power of L. In this paper various convergence results are obtained for the corr…
Let X be a smooth complex projective variety of dimension d. It is classical that ample line bundles on X satisfy many beautiful geometric, cohomological, and numerical properties that render their behavior particularly tractable. By contrast, examples due to Cutkosky and others have led to the common impression that t…
This paper gives an algebraic conjecture which is shown to be equivalent to Thurston's Geometrization Conjecture for closed, orientable 3-manifolds. It generalizes the Stallings-Jaco theorem which established a similar result for the Poincare Conjecture. The paper also gives two other algebraic conjectures; one is equi…
We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum-Connes conjecture. In particula…
We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum-Connes conjecture. The Burghelea conjecture implies the Bass conjecture. We state two conjectures about groups of finite asymptotic dimension, which tog…