Algebraic Deformations of Polarized Varieties
Let V be a projectively embeddable complete non-singular variety of dimension n > 1. Let f be a projective embedding of V, U a non-singular variety, W a non-singular variety and φ a morphism of W onto U such that φ-1(u0) = f(V) for some point u0 of U. Denote by ∑(V) the set of all those complete non-singular fibres φ-1(u), u ∈ U, as we consider all possible (f, U, W). Suppose that we call members of ∑(V) (algebraic) deformations of V and propose to study ∑(V) from the stand point of algebraic geometry, as a generalization of the case of curves. This has been taken up at least locally by Kodaira, Spencer, Kuranishi and others in the case of characteristic 0 from a little more general point of view of complex manifolds (cf. [9] and references given in [16]).
Note on the Intersection of an Algebraic Variety with the Generic Hyperplane
Let V ( r>1 ) be an algebraic variety immersed in the projective space L , k a field of definition for V, and W 1 a generic hyperplane with respect to k in L . Then it is well known that the intersection HV is defined and is an irreducible variety" In this case the question arises that the variety may get a new singular point other than that o f V . When the characteristic p of the universal domain is 0 , we know that such a case cannot take place by the second theorem o f B e rtin i. In this note we shall show that it is also true even when the case To discuss this problem it is sufficient to consider the case when V is lying in the affine space SA'. Let
Techno-economic analysis of solar thermal power plants using liquid sodium as heat transfer fluid
Abstract Solar thermal power plants with central receiver and thermal storage are expected to be one key technology in future electricity generation, because they are renewable and due to the thermal storage independent of the current solar radiation. State-of-the-art solar power plants often use molten nitrate salts as heat transfer fluid. The use of liquid sodium instead leads to lower electricity generation costs. Sodium has a high thermal conductivity and thus large heat transfer rates are possible. Hence, a smaller absorber surface is sufficient for the same thermal power. As a result, the sodium receiver achieves a higher efficiency at lower investment cost. Additionally, the aiming strategy, which reduces the peak heat flux on molten salt receivers isn’t necessary for sodium. Even at high heat flux densities, the absorber tubes will be cooled sufficiently due to the high heat transfer coefficients. Therefore, the sodium receiver in this analysis is designed for one single aim point, resulting in a heat flux density of q mean = 1.06 MW / m 2 and q peak = 2.99 MW / m 2 . The state-of-the-art system with molten salt considers q mean = 0.51 MW / m 2 and q peak = 1.0 MW / m 2 . The presented techno-economic analysis of two sodium based concepts compared to a reference system with molten salt results in up to 16% lower electricity generation costs.