Suppose given an holomorphic and Hamiltonian action of a compact torus $T$ on polarized Hodge manifold $M$. Assume that the lifts to quantizing line bundle, so there is induced unitary representation associated Hardy space. If in addition moment map nowhere zero, for each weight $\boldsymbol{\nu}$ $\boldsymbol{\nu}$-th isotypical component space polarization finite-dimensional. Assuming transve...

The main goal of this note is to begin a systematic study on conic-line arrangements in the complex projective plane. We show de Bruijn-Erd\H{o}s-type inequality and Hirzebruch-type for certain class having ordinary singularities. will also study, detail, context geography log-surfaces free divisors sense Saito.

We carry out the programme of R. Liouville [18] to construct an explicit local obstruction to the existence of a Levi–Civita connection within a given projective structure [Γ] on a surface. The obstruction is of order 5 in the components of a connection in a projective class. It can be expressed as a point invariant for a second order ODE whose integral curves are the geodesics of [Γ] or as a w...

The aim of phishing is tracing the users' s private information without their permission by designing a new website which mimics the trusted website. The specialists of information technology do not agree on a unique definition for the discriminative features that characterizes the phishing websites. Therefore, the number of reliable training samples in phishing detection problems is limited. M...

Let k be a perfect field of positive characteristic and Z an effective Cartier divisor in the projective line over with complement U. In this note, we establish some results about formal deformation theory overconvergent isocrystals on U fixed “local monodromy” along Z. En route, show that Hochschild cochain complex governs deformations module arbitrary associative algebra. We also relate to de...