Related papers: A simple proof of Dahmen's conjectures

It is well-known that Lagrange's four-square theorem, stating that every natural number may be written as the sum of four squares, may be proved using methods from the classical theory of modular forms and theta functions. We revisit this…

In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…

In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial graphs. Conjecture~2, which implies Conjecture~1, deals with…

We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover…

In this note we prove that the crepant transformation conjecture for a crepant birational transformation of Lawrence toric DM stacks studied in \cite{CIJ} implies the monodromy conjecture for the associated wall crossing of the symplectic…

We introduce a notion of normal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this normal form exists and is unique when ambient space is two-dimensional. From this…

We survey recent results about the Torelli question for holomorphic-symplectic varieties. Following are the main topics. A Hodge theoretic Torelli theorem. A study of the subgroup W, of the isometry group of the weight 2 Hodge structure,…

A new approach to analyze the properties of the energy-momentum tensor $T(z)$ of conformal field theories on generic Riemann surfaces (RS) is proposed. $T(z)$ is decomposed into $N$ components with different monodromy properties, where $N$…

We study semantic and syntactic properties of spherical orders and their elementary theories, including finite and dense orders and their theories. It is shown that theories of dense $n$-spherical orders are countably categorical and…

A conjecture of Kato says that the monodromy operator on the cohomology of a semi-stable degeneration of projective varieties is represented by an algebraic cycle on the special fiber of a normal crossing model of the fiber product…

We consider singular foliations whose holonomy groupoid may be nicely decomposed using Lie groupoids (of unequal dimension). We show that the Baum-Connes conjecture can be formulated in this setting. This conjecture is shown to hold under…

We prove the weight-monodromy conjecture for varieties which are p-adically uniformized by a product of the Drinfeld upper half spaces. It is an easy consequence of Dat's work on the cohomology complex of the Drinfeld upper half space.

J.C.Lagarias (2000) conjectured that if $\mu$ is a complex measure on p-dimensional Euclidean space with a uniformly discrete support and its spectrum (Fourier transform) is also a measure with a uniformly discrete support, then the support…

We prove a big monodromy result for a smooth family of complex algebraic surfaces of general type, with invariants p_g=q=1 and K^2=3, that has been introduced by Catanese and Ciliberto. This is accomplished via a careful study of…

We construct an effective algorithmic method to compute the homological monodromy of a complex polynomial which is tame. As an application we show the existence of conjugated polynomials in a number field which are not topologically…

The monodromy conjecture is a mysterious open problem in singularity theory. Its original version relates arithmetic and topological/geometric properties of a multivariate polynomial $f$ over the integers, more precisely, poles of the…

The SL(2,C)-representation varieties of punctured surfaces form natural families parameterized by holonomies at the punctures. In this paper, we first compute the loci where these varieties are singular for the cases of one-holed and…

We investigate a strong version of the integral Tate conjecture for 1-cycles on the product of a curve and a surface over a finite field, under the assumption that the surface is geometrically $CH_0$-trivial. By this we mean that over any…

A conjecture, recently stated by Flach and Morin, relates the action of the monodromy on the Galois invariant part of the p-adic Beilinson-Hyodo-Kato cohomology of the generic fiber of a scheme defined over a DVR of mixed characteristic to…

Let M be a meromorphic connection with poles along a smooth divisor D in a smooth algebraic variety. Let Sol M be the solution complex of M. We prove that the good formal decomposition locus of M coincides with the locus where the…