Book Review: Resolution of singularities; Lectures on resolution of singularities
نویسندگان
چکیده
منابع مشابه
Review of “ Alterations and resolution of singularities ”
The book contains a collection of articles by participants of the Working Week on Resolution of Singularities held at Obergurgl in Tirol, September 7-14, 1997. It is dedicated to Oscar Zariski, the founder of the school of algebraic geometry in the United States. During his long career as a mathematician he obtained ground-breaking results in algebra and algebraic geometry. Many years of his ca...
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We show that a class of 3+1 dimensional Friedmann-RobertsonWalker cosmologies can be embedded within a variety of solutions of string theory. In some realizations the apparent singularities associated with the big bang or big crunch are resolved at non-singular horizons of higher-dimensional quasi-black hole solutions (with compactified real time); in others plausibly they are resolved at D-bra...
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For a certain class of varieties X, we derive a formula for the valuation dX on the arc space L(Y ) of a smooth ambient space Y , in terms of an embedded resolution of singularities. A simple transformation rule yields a formula for the geometric Poincaré series. Furthermore, we prove that for this class of varieties, the arithmetic and the geometric Poincaré series coincide. We also study the ...
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We study time–dependent backgrounds in the low energy regimes of string theories. In particular the emphasis is on the general study of exotic phenomena such as positive acceleration and gravitational bounces. We generalize the usual Hawking–Penrose cosmological singularity theorems to higher–dimensional spacetimes and discuss their implications for time–dependent solutions in supergravity theo...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2011
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-10-01301-7