Estimates of the number of rational mappings from a fixed variety to varieties of general type

First we find effective bounds for the number of dominant rational maps $f:X \rightarrow Y$ between two fixed smooth projective varieties with ample canonical bundles. The bounds are of the type $\{A \cdot K_X^n\}^{\{B \cdot K_X^n\}^2}$, where $n=dimX$, $K_X$ is the canonical bundle of $X$ and $A,B$ are some constants, depending only on $n$. Then we show that for any variety $X$ there exist numbers $c(X)$ and $C(X)$ with the following properties: For any threefold $Y$ of general type the number of dominant rational maps $f:X \r Y$ is bounded above by $c(X)$. The number of threefolds $Y$, modulo birational equivalence, for which there exist dominant rational maps $f:X \r Y$, is bounded above by $C(X)$. If, moreover, $X$ is a threefold of general type, we prove that $c(X)$ and $C(X)$ only depend on the index $r_{X_c}$ of the canonical model $X_c$ of $X$ and on $K_{X_c}^3$.Comment: A revised version. The presentation of results and proofs has been improved. AMS-TeX, 19 page

Plane curves with a big fundamental group of the complement

Let C \s \pr^2 be an irreducible plane curve whose dual C^* \s \pr^{2*} is an immersed curve which is neither a conic nor a nodal cubic. The main result states that the Poincar\'e group \pi_1(\pr^2 \se C) contains a free group with two generators. If the geometric genus $g$ of $C$ is at least 2, then a subgroup of $G$ can be mapped epimorphically onto the fundamental group of the normalization of $C$, and the result follows. To handle the cases $g=0,1$, we construct universal families of immersed plane curves and their Picard bundles. This allows us to reduce the consideration to the case of Pl\"ucker curves. Such a curve $C$ can be regarded as a plane section of the corresponding discriminant hypersurface (cf. [Zar, DoLib]). Applying Zariski--Lefschetz type arguments we deduce the result from `the bigness' of the $d$-th braid group $B_{d,g}$ of the Riemann surface of $C$.Comment: 23 pages LaTeX. A revised version. The unnecessary restriction $d \ge 2g - 1$ of the previous version has been removed, and the main result has taken its final for

A comparative study on the effects of a pesticide (cypermethrin) and two metals (copper, lead) to serum biochemistry of Nile tilapia, Oreochromis niloticus

The present study was designed to compare the responses in freshwater fish Oreochromis niloticus exposed to a synthetic pyrethroid, cypermethrin (CYP); an essential metal, copper (Cu); and a nonessential metal, lead (Pb). Fish were exposed to 0.05 μg/l CYP, 0.05 mg/l Cu, and 0.05 mg/l Pb for 4 and 21 days, and the alterations in serum enzyme activities, metabolite, and ion levels were determined. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) activities increased in response to CYP, Cu, and Pb exposures at both exposure periods. While elevations in alkaline phosphatase (ALP) and lactate dehydrogenase (LDH) activities and in cholesterol level were observed in pesticide-exposed fish at 4 and 21 days, they increased in Cu- and Pb-exposed fish at 21 days. Although metal-exposed fish showed increases in cortisol and glucose levels at 4 days followed by a return to control levels at the end of the exposure period, their levels elevated in pesticide-exposed fish at both exposure periods. Total protein levels decreased in Pb- and pesticide-exposed fish at 21 days. Na+ and Cl− levels decreased in pesticide-exposed fish at both exposure periods and in Cu- and Pb-exposed fish at 21 days. The exposures of pesticide and metals caused an elevation in K+ level at the end of the exposure period. The present study showed that observed alterations in all serum biochemical parameters of fish-treated pesticide were higher than those in fish exposed to metals

Overview of the MOSAiC expedition—Atmosphere

With the Arctic rapidly changing, the needs to observe, understand, and model the changes are essential. To support these needs, an annual cycle of observations of atmospheric properties, processes, and interactions were made while drifting with the sea ice across the central Arctic during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition from October 2019 to September 2020. An international team designed and implemented the comprehensive program to document and characterize all aspects of the Arctic atmospheric system in unprecedented detail, using a variety of approaches, and across multiple scales. These measurements were coordinated with other observational teams to explore cross-cutting and coupled interactions with the Arctic Ocean, sea ice, and ecosystem through a variety of physical and biogeochemical processes. This overview outlines the breadth and complexity of the atmospheric research program, which was organized into 4 subgroups: atmospheric state, clouds and precipitation, gases and aerosols, and energy budgets. Atmospheric variability over the annual cycle revealed important influences from a persistent large-scale winter circulation pattern, leading to some storms with pressure and winds that were outside the interquartile range of past conditions suggested by long-term reanalysis. Similarly, the MOSAiC location was warmer and wetter in summer than the reanalysis climatology, in part due to its close proximity to the sea ice edge. The comprehensiveness of the observational program for characterizing and analyzing atmospheric phenomena is demonstrated via a winter case study examining air mass transitions and a summer case study examining vertical atmospheric evolution. Overall, the MOSAiC atmospheric program successfully met its objectives and was the most comprehensive atmospheric measurement program to date conducted over the Arctic sea ice. The obtained data will support a broad range of coupled-system scientific research and provide an important foundation for advancing multiscale modeling capabilities in the Arctic