The Vanishing Original

Vanishing Vanishing Cycles

If A• is a bounded, constructible complex of sheaves on a complex analytic space X, and f : X → C and g : X → C are complex analytic functions, then the iterated vanishing cycles φg[−1](φf [−1]A •) are important for a number of reasons. We give a formula for the stalk cohomology H∗(φg[−1]φf [−1]A •)x in terms of relative polar curves, algebra, and the normal Morse data and micro-support of A•.

ON THE VANISHING OF DERIVED LOCAL HOMOLOGY MODULES

Let $R$ be a commutative Noetherian ring, $fa$ anideal of $R$ and $mathcal{D}(R)$ denote the derived category of$R$-modules. For any homologically bounded complex $X$, we conjecture that$sup {bf L}Lambda^{fa}(X)leq$ mag$_RX$. We prove thisin several cases. This generalize the main result of Hatamkhani and Divaani-Aazar cite{HD} for complexes.

The Vanishing Protestant Majority

1 Advantages of using the GSS include a) its measurement of Protestants has not changed over the years, b) its high quality (e.g. its high overall response rate and low item non-response on religion), and c) its large sample size (over 43,000 respondents in 1972-2002).

The Vanishing Girl Child

The world’s vanishing lakes

Watery planet: The world’s lakes may be small in volume compared with the oceans, but they are widespread and provide important habitat as well as valuable ecosystem services. This map shows the world’s lakes with surface areas of 10 hectares or more. The large, dark blue areas in Canada refl ect the high concentration of lakes in those regions. (Image: HydroLAB, McGill University.) Maps of the...