Let M be a compact symplectic manifold on which a compact torus T acts Hamiltonialy with a moment map μ. Suppose there exists a symplectic involution θ : M → M , such that μ ◦ θ = −μ. Assuming that 0 is a regular value of μ, we calculate the character of the action of θ on the cohomology of M in terms of the character of the action of θ on the symplectic reduction μ(0)/T of M . This result gene...

This paper classifies surfaces of general type S with pg = q = 1 having an involution i such that S/i has non-negative Kodaira dimension and that the bicanonical map of S factors through the double cover induced by i. It is shown that S/i is regular and either: a) the Albanese fibration of S is of genus 2 or b) S has no genus 2 fibration and S/i is birational to a K3 surface. For case a) a list...

The main goal of this paper is to propose an approach inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO involution-reflection. Our based reduction problem matrix form and solution Sturm-Liouville operator by developing method mappings. obtained contains weight, which causes qualitative difficulties in study ...

A theorem is proved on the structure of the group of isometries of an Hermitian map b : V × V → W , where V and W are vector spaces over a finite field of odd order. Also a Las Vegas polynomial-time algorithm is presented which, given an Hermitian map, finds generators for, and determines the structure of its isometry group. The algorithm can be adapted to construct the intersection of the memb...

We show that any pointed, peordered module map BFgr(E)→BFgr(F) between Bowen-Franks modules of finite graphs can be lifted to a unital, graded, diagonal preserving ⁎-homomorphism Lℓ(E)→Lℓ(F) the corresponding Leavitt path algebras over commutative unital ring with involution ℓ. Specializing case when ℓ is field, we establish fullness part Hazrat's conjecture about functor from ℓ-algebras preord...

We show that over a field of characteristic 2 a central simple algebra with orthogonal involution that decomposes into a product of quaternion algebras with involution is either anisotropic or metabolic. We use this to define an invariant of such orthogonal involutions in characteristic 2 that completely determines the isotropy behaviour of the involution. We also give an example of a non-total...

We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we prove that in this region the area occupied by stable periodic orbits remains positive. The main device is the construction of an induced map on a domain wit...

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a carefull analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate th...

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a careful analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate the...

The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras with involution are studied. It is proven that, up to degree 16, over any extension over which the algebra splits, the involution is adjoint to...