We construct Deligne-Mumford stacks Pd,g representable over Mg parametrizing Néron models of Jacobians as follows. Let K = k(B) be a one-dimensional function field and let XK be a smooth genus-g curve over K admitting stable minimal model over B. The Néron model N(PicXK) −→ B is the base change of Pd,g via the moduli map B −→ Mg of f , that is: N(Pic XK) ∼= Pd,g ×Mg B. Pd,g is compactified by a...

We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson generalization of the reduction of symplectic manifolds with symmetry. Having as basic tools the equivariant momentum maps of Poisson actions, the double group of a Poisson-Lie group and the reduction of Poisson manifolds with symmetry, we show how one can induce a Poisson action admitting an equ...

We study rational double Hurwitz cycles, i.e. loci of marked rational stable curves admitting a map to the projective line with assigned ramification profiles over two fixed branch points. Generalizing the phenomenon observed for double Hurwitz numbers, such cycles are piecewise polynomial in the entries of the special ramification; the chambers of polynomiality and wall crossings have an expli...

We construct modular Deligne-Mumford stacks Pd,g representable over Mg parametrizing Néron models of Jacobians as follows. Let B be a smooth curve andK its function field, let XK be a smooth genus-g curve over K admitting stable minimal model over B. The Néron model N(Pic XK) → B is then the base change of Pd,g via the moduli map B −→ Mg of f , i.e.: N(Pic XK) ∼= Pd,g ×Mg B. Moreover Pd,g is co...

This paper deals with variational inclusions of the form: 0 ∈ f(x)+F (x) where f is a single function admitting a second order Fréchet derivative and F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (xk) satisfying 0 ∈ f(xk)+ ∑M i=1 ai∇f ( xk+βi(xk+1−xk) ) (xk+1−xk)+F (xk+1) where the single-valued function involved in this relation is an approximation of the ...

Let G and H ⊂ G be connected reductive real algebraic groups defined over Q, and admitting no nontrivial Q-characters. Let Γ ⊂ G(Q) be an arithmetic lattice in G, and π : G→ Γ\G be the natural quotient map. Let μH denote the H-invariant probability measure on the closed orbit π(H). Suppose that π(Z(H)) is compact, where Z(H) denotes the centralizer of H in G. We prove that the set {μH · g : g ∈...

We construct modular Deligne-Mumford stacks Pd,g representable over Mg parametrizing Néron models of Jacobians as follows. Let B be a smooth curve and K its function field, let XK be a smooth genus-g curve over K admitting stable minimal model over B. The Néron model N(PicXK ) → B is then the base change of Pd,g via the moduli map B −→ Mg of f , i.e.: N(PicXK ) ∼= Pd,g ×Mg B. Moreover Pd,g is c...

Estimating maps among large collections of objects (e.g., dense correspondences across images and 3D shapes) is a fundamental problem across a wide range of domains. In this paper, we provide theoretical justifications of spectral techniques for the map synchronization problem, i.e., it takes as input a collection of objects and noisy maps estimated between pairs of objects along a connected ob...

Let f be an essential map of Sn−1 into itself (i.e., f is not homotopic to a constant mapping) admitting an extension mapping the closed unit ball B n into Rn. Then, for every interior point y of Bn, there exists a point x in f −1(y) such that the image of no neighborhood of x is contained in a coordinate half space with y on its boundary. Under additional conditions, the image of a neighborhoo...

An edge-magic total labeling on G is a one-to-one map λ from V (G) ∪ E(G) onto the integers 1, 2, . . . , |V (G) ∪ E(G)| with the property that, given any edge (x, y), λ(x) + λ(x, y) + λ(y) = k for some constant k. The labeling is strong if all the smallest labels are assigned to the vertices. Enomoto et al. proved that a graph admitting a strong labeling can have at most 2|V (G)| − 3 edges. In...