New symplectic V-manifolds of dimension four via the relative compactified Prymian

Three new examples of 4-dimensional irreducible symplectic V-manifolds are constructed. Two of them are relative compactified Prymians of a family of genus-3 curves with involution, and the third one is obtained from a Prymian by Mukai's flop. They have the same singularities as two of Fujiki's examples, namely, 28 isolated singular points analytically equivalent to the Veronese cone of degree 8, but a different Euler number. The family of curves used in this construction forms a linear system on a K3 surface with involution. The structure morphism of both Prymians to the base of the family is a Lagrangian fibration in abelian surfaces with polarization of type (1,2). No example of such fibration is known on nonsingular irreducible symplectic varieties.Comment: 28 page

Series of rational moduli components of stable rank 2 vector bundles on P3\mathbb{P}^3

We study the problem of rationality of an infinite series of components, the so-called Ein components, of the Gieseker-Maruyama moduli space $M(e,n)$ of rank 2 stable vector bundles with the first Chern class $e=0$ or -1 and all possible values of the second Chern class $n$ on the projective 3-space. The generalized null correlation bundles constituting open dense subsets of these components are defined as cohomology bundles of monads whose members are direct sums of line bundles of degrees depending on nonnegative integers $a,b,c$, where $b\ge a$ and $c>a+b$. We show that, in the wide range when c>2a+b-e,\b>a,\ (e,a)\ne(0,0), the Ein components are rational, and in the remaining cases they are at least stably rational. As a consequence, the union of the spaces $M(e,n)$ over all $n\ge1$ contains an infinite series of rational components for both $e=0$ and $e=-1$. Explicit constructions of rationality of Ein components under the above conditions on $e,a,b,c$ and, respectively, of their stable rationality in the remaining cases, are given. In the case of rationality, we construct universal families of generalized null correlation bundles over certain open subsets of Ein components showing that these subsets are fine moduli spaces. As a by-product of our construction, for $c_1=0$ and $n$ even, they provide, perhaps the first known, examples of fine moduli spaces not satisfying the condition "$n$ is odd", which is a usual sufficient condition for fineness

Construction of stable rank 2 vector bundles on P3\mathbb{P}^3 via symplectic bundles

In this article we study the Gieseker-Maruyama moduli spaces $\mathcal{B}(e,n)$ of stable rank 2 algebraic vector bundles with Chern classes $c_1=e\in\{-1,0\},\ c_2=n\ge1$ on the projective space $\mathbb{P}^3$. We construct two new infinite series $\Sigma_0$ and $\Sigma_1$ of irreducible components of the spaces $\mathcal{B}(e,n)$, for $e=0$ and $e=-1$, respectively. General bundles of these components are obtained as cohomology sheaves of monads, the middle term of which is a rank 4 symplectic instanton bundle in case $e=0$, respectively, twisted symplectic bundle in case $e=-1$. We show that the series $\Sigma_0$ contains components for all big enough values of $n$ (more precisely, at least for $n\ge146$). $\Sigma_0$ yields the next example, after the series of instanton components, of an infinite series of components of $\mathcal{B}(0,n)$ satisfying this property

Modeling of optical properties of hybrid metal-organic nanostructures

To model spectral characteristics of hybrid metal-organic nanostructures, the extended Mie theory was used, which makes it possible to calculate the extinction efficiency factor (Qext) and the scattering efficiency factor in the near zone (QNF) of two-layer spherical particles placed in an absorbing matrix. Two-layer plasmon nanospheres consisting of a metallic core (Ag, Cu) coated with dielectric shells and located into the copper phthalocyanine (CuPc) matrix were considered. The influence of dielectric shell thickness and refractive index on the characteristics of the surface plasmon resonance of absorption (SPRA) was studied. The possibility of the SPRA band tuning by changing the optical and geometrical parameters of dielectric shells was shown. It was established that dielectric shells allow to shift the surface plasmon resonance band of plasmonic  nanoparticles absorption both  to  short-  and  long-wavelength  spectral  range  depending on the relation between shell and matrix refractive indexes.To model spectral characteristics of hybrid metal-organic nanostructures, the extended Mie theory was used, which makes it possible to calculate the extinction efficiency factor (Qext) and the scattering efficiency factor in the near zone (QNF) of two-layer spherical particles placed in an absorbing matrix. Two-layer plasmon nanospheres consisting of a metallic core (Ag, Cu) coated with dielectric shells and located into the copper phthalocyanine (CuPc) matrix were considered. The influence of dielectric shell thickness and refractive index on the characteristics of the surface plasmon resonance of absorption (SPRA) was studied. The possibility of the SPRA band tuning by changing the optical and geometrical parameters of dielectric shells was shown. It was established that dielectric shells allow to shift the surface plasmon resonance band of plasmonic  nanoparticles absorption both  to  short-  and  long-wavelength  spectral  range  depending on the relation between shell and matrix refractive indexes

New moduli components of rank 2 bundles on projective space

We present a new family of monads whose cohomology is a stable rank two vector bundle on $\mathbb{P}^3$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used to construct a new infinite series of rational moduli components of stable rank two vector bundles with trivial determinant and growing second Chern class. We also prove that the moduli space of stable rank two vector bundles with trivial determinant and second Chern class equal to 5 has exactly three irreducible rational components