7425 papers
This paper introduces the concept of abelian-normal numbers by adapting abelian complexity functions to digit expansions, constructs a non-normal analogue of Champernowne's constant that satisfies this new property, and proposes open problems regarding its behavior.
This paper classifies all -bundles over smooth projective rational surfaces that possess a maximal neutral component of their automorphism group, valid over any algebraically closed field of characteristic zero.
This paper establishes that connected sums of Artinian Gorenstein generalized Golod rings are good, providing specific criteria and conditions under which such rings are good while also presenting examples of bad Artinian Gorenstein local rings to advance the understanding of a question posed by L. Avramov.
This paper establishes the theoretical foundation for constructing lattice algorithms that achieve optimal convergence rates for multivariate approximation in periodic spaces with general weight parameters, specifically addressing the needs of PDE applications involving POD and SPOD weights.
This paper establishes that a smooth quartic surface over a number field contains only finitely many rational bitangents by leveraging the geometry of its associated quartic double solid, while simultaneously demonstrating that its set of quadratic algebraic points is Zariski-dense.
This paper addresses the mathematical challenge of defining "natural" axiomatic theories to explain their empirical pre-well-ordering by consistency strength, surveying strategies involving reflection principles, ordinal analysis, and recursion theory while highlighting open problems and future research directions.
This paper investigates quantum dependence and independence concepts, particularly regarding hidden variables and non-locality, by applying team semantics and probabilistic team semantics to derive new results in independence logic and probabilistic independence logic.
This paper employs log geometry to investigate the smoothability of genus zero twisted stable maps to stacky curves relative to marked points, with applications to smoothing semi-log canonical fibered surfaces with marked singular fibers.
The authors establish a general criterion for the uniqueness of Serre-invariant stability conditions in low-dimensional fractional Calabi-Yau categories, applying it to the Kuznetsov component of cubic threefolds to prove that all known stability conditions lie in a single orbit and that the moduli space of Ulrich bundles of rank at least 2 is irreducible.
This paper establishes the abundance conjecture for projective semi-log canonical (slc) surfaces over arbitrary fields of positive characteristic by leveraging Tanaka's results on log canonical surfaces and Hacon-Xu's normalization techniques, while also deriving applications for dlt threefold pairs and mixed characteristic families.
This paper proves that moduli spaces of semistable vector bundles with coprime rank and degree over a non-singular real projective curve are maximal real algebraic varieties if and only if the underlying curve is maximal, establishing this result through the stronger property of Hodge-expressivity.
This paper establishes that the rational Chow motive of O'Grady's six-dimensional hyper-Kähler varieties, constructed as symplectic resolutions of singular moduli spaces on abelian surfaces, is generated by the motive of the underlying surface, thereby confirming the Hodge and Tate conjectures for these varieties.
The paper demonstrates that flat families of stable 3-folds fail to form proper moduli spaces in any positive characteristic , a result that simultaneously yields log canonical 4-fold pairs with non-weakly normal log canonical centers.
This paper establishes a unified framework for proving sharp thresholds in Ramsey properties by modeling them as non-colourability of auxiliary hypergraphs, successfully applying this method to demonstrate sharp thresholds for graph Ramsey properties involving cliques and cycles, as well as arithmetic Ramsey properties related to van der Waerden's and Schur's theorems.
This paper demonstrates that while Jensen's square principle is non-compact at , the weak square principle is actually compact at singular cardinals of uncountable cofinality under mild hypotheses, contrasting with the behavior at .
This paper proves that the fundamental group of a closed orientable irreducible 3-manifold admitting a co-orientable taut foliation with one-sided branching is left orderable.
The paper establishes that the fundamental group of a closed, orientable, irreducible 3-manifold is left orderable if the manifold admits a co-orientable taut foliation with orderable cataclysm, thereby providing an elementary proof for the left orderability of fundamental groups in the presence of Anosov or pseudo-Anosov flows and extending this result to infinitely many Dehn fillings.
This paper proves Sargsyan's conjecture that for any regular Suslin cardinal in , if the associated pointclass is inductive-like, then there exists no sequence of distinct -Suslin sets of length .
This paper establishes that in NATP theories, Kim-dividing over models is always witnessed by coheir Morley sequences, leading to key corollaries regarding quasi-dividing and the characterization of Kim-independence, while also clarifying the relationship between these concepts and Mutchnik's recent work on -NDCTP theories.
This paper establishes that for a conilpotent coalgebra , the inclusion of comodules into -modules and the forgetful functor from contramodules to -modules both induce fully faithful triangulated functors on appropriate bounded derived categories if and only if the Ext-groups are finite-dimensional for all , a condition the authors term "weakly finitely Koszul."