In this paper we will suggest a construction for height functions for line bundles on arithmetic varieties. Following the philosophy of [BoGS] heights should be objects in arithmetic geometry analogous to degrees in algebraic geometry. So let K be a number field, OK its ring of integers and X /OK an arithmetic variety, i.e. a regular scheme, projective and flat over OK , whose generic fiber X/K...

Topological Chern-Simons (CS) and BF theories and their holomorphic analogues are discussed in terms of de Rham and Dolbeault cohomologies. We show thatČech cohomology provides another useful description of the above topological and holomorphic field theories. In particular, all hidden (nonlocal) symmetries of non-Abelian CS and BF theories can be most clearly seen in thě Cech approach. We cons...

H. Sato introduced a Schwarzian derivative of a contactomorphism of R 3 and and with T. Ozawa described its basic properties. In this note their construction is extended to all odd dimensions and to non-flat contact projective structures. The contact projective Schwarzian derivative of a contact projective structure is defined to be a cocycle of the contactomorphism group taking values in the s...

The aim of this paper is to define an $L^p$ space intuitionistic fuzzy observables. We work in $({\mathcal F}, {\bf m})$ with product, where $\mathcal F$ a family events and ${\bf m}$ state. prove that the corresponding pseudometric $\rho_{IF}$ space.

Ellingsrud and Peskine (1989) proved that there exists a bound on the degree of smooth non general type surfaces in P. The latest proven bound is 52 by Decker and Schreyer in 2000. In this paper we consider bounds on the degree of a quasismooth non-general type surface in weighted projective 4-space. We show that such a bound in terms of the weights exists, and compute an explicit bound in simp...

Let $X$ be a complex manifold and $L$ holomorphic line bundle on $X$. Assume that is semi-positive, namely admits smooth Hermitian metric with semi-positive Chern curvature. $Y$ compact K\"ahler submanifold of such the restriction to topologically trivial. We investigate obstruction for unitary flat neighborhood in As an application, example, we show existence nef, big, non non-singular project...

In this paper we make use of counterpart semantics to prove an original incompleteness result in quantified modal logic (QML), that is, the system QE .K+BF based on free logic and containing the Barcan formula is incomplete with respect to Kripke semantics. This incompleteness result extends to the system QE .K+CBF+BF obtained by adding the converse of the Barcan formula to QE .K+BF .