Desingularization Strategies for Three-Dimensional Vector - download pdf or read online

By Felipe Cano Torres

ISBN-10: 0387179445

ISBN-13: 9780387179445

ISBN-10: 3540179445

ISBN-13: 9783540179443

For a vector box #3, the place Ai are sequence in X, the algebraic multiplicity measures the singularity on the starting place. during this learn monograph a number of innovations are given to make the algebraic multiplicity of a 3-dimensional vector box lessen, through permissible blowing-ups of the ambient house, i.e. ameliorations of the sort xi=x'ix1, 2<i<s, xi=x'i, i>s. A logarithmic perspective is taken, marking the outstanding divisor of every blowing-up and by way of contemplating in basic terms the vector fields that are tangent to this divisor, rather than the full tangent sheaf. the 1st a part of the ebook is dedicated to the logarithmic history and to the permissible blowing-ups. the most half corresponds to the keep watch over of the algorithms for the desingularization innovations by way of numerical invariants encouraged by way of Hironaka's attribute polygon. merely uncomplicated wisdom of neighborhood algebra and algebraic geometry is believed of the reader. The pathologies we discover cut back vector fields are analogous to pathologies within the challenge of aid of singularities in attribute p. for this reason the booklet is in all likelihood attention-grabbing either within the context of answer of singularities and in that of vector fields and dynamical platforms.

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3) us the change o f the anunified Lemma. 9). of significant a winning strategy differences in the type 0-1 technical = 2. be a n o r m a l i z e d o£ base and l e t &(~,E,p) and us suppose t h a t (s,t) ~ ~ 2 o . Let e(E)=2. 1) X ( k. 3). 7) and i f T-2 or T-4 then m ( O ' , E ' , p ' ) = ~ , Let Pl = (x'Y'Zl)" = z + kxSy t Then one has t h a t Pl i s n o r m a l i z e d . b) A ( ~ , E , p 1) c is Proof. a vertex A(~,E,p) and e v e r y v e r t e x o£ & ~ , E , p ) of A(D,E,Pl). a) trivial.

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3) cate P^ and P^' The e x i s t e n c e the existence wing de£inition Definition. ,x) that ~p has n o r m a l must conditions and a posteriori one w a n t s t o let P adapted be a r . s . 1) E" i f £ with E at the The f o l i o - and ( 3 . 3 . 9 . 2 ) P be a c l o s e d to indi- point o£ Y. 3) conditions ~ r-1 "Vy(ai) ~ r if if o f OX, A or suited P. the pair (E,Y) is so i n definition fbr for issatis£ied: ~ B. V y ( a i ) ~ i g B-A such t h a t i ( P point + i ~A ai~laxi" i g A on i exist p. 2) i ~ B.

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Desingularization Strategies for Three-Dimensional Vector Fields by Felipe Cano Torres


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