منابع مشابه
Rational Cuspidal Curves
It is the product of my playing with beautiful geometric objects called rational cuspidal curves over the past two years. I would like to thank everyone who has contributed to this thesis. I owe so much to everyone who has ever taught me mathematics. Thank you for inspiring me and for providing me with the skills necessary to complete this thesis. To my friends and fellow students at Abel, than...
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We compute the Euler characteristics of the moduli spaces of abelian vortices on curves with nodal and cuspidal singularities. This generalizes our previous work where only nodes were taken into account. The result we obtain is again consistent with the expected reconciliation between the vortex picture of D2-D0 branes and the proposal by Gopakumar and Vafa.
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1 Rational Geometric Fundamental Groups Let K be a nitely generated eld with separable closure K s and absolute Galois group G K : By a curve C=K we always understand a smooth geometrically irreducible projective curve. Let F(C) be its function eld and let (C) be the Galois group of the maximal unramiied extension of F(C): We have the exact sequence 1 ! g (C) ! (C) ! G K ! 1 (?) where g (C) is ...
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where Πg(C) is the geometric (profinite) fundamental group of C×Spec(Ks) (i.e. Πg(C) is equal to the Galois group of the maximal unramified extension of F (C)⊗Ks). This sequence induces a homomorphism ρC from GK to Out(Πg(C)) which is the group of automorphisms modulo inner automorphisms of Πg(C). It is well known that ρC is an important tool for studying C. For instance, it determines C up to ...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 1999
ISSN: 0024-6093
DOI: 10.1112/s0024609398005323