scholarly journals Geometry of Puiseux expansions

2008 ◽  
Vol 93 (3) ◽  
pp. 263-280
Author(s):  
Maciej Borodzik ◽  
Henryk Żołądek
Keyword(s):  
1968 ◽  
Vol 9 (2) ◽  
pp. 146-151 ◽  
Author(s):  
F. J. Rayner

Letkbe any algebraically closed field, and denote byk((t)) the field of formal power series in one indeterminatetoverk. Letso thatKis the field of Puiseux expansions with coefficients ink(each element ofKis a formal power series intl/rfor some positive integerr). It is well-known thatKis algebraically closed if and only ifkis of characteristic zero [1, p. 61]. For examples relating to ramified extensions of fields with valuation [9, §6] it is useful to have a field analogous toKwhich is algebraically closed whenkhas non-zero characteristicp. In this paper, I prove that the setLof all formal power series of the form Σaitei(where (ei) is well-ordered,ei=mi|nprt,n∈ Ζ,mi∈ Ζ,ai∈k,ri∈ Ν) forms an algebraically closed field.


1990 ◽  
Vol 24 (4) ◽  
pp. 33-41
Author(s):  
V. Baladi ◽  
J.-P. Guillement
Keyword(s):  

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Thomas W. Grimm ◽  
Chongchuo Li

Abstract We study the backreaction effect of a large axion field excursion on the saxion partner residing in the same $$ \mathcal{N} $$ N = 1 multiplet. Such configurations are relevant in attempts to realize axion monodromy inflation in string compactifications. We work in the complex structure moduli sector of Calabi-Yau fourfold compactifications of F-theory with four-form fluxes, which covers many of the known Type II orientifold flux compactifications. Noting that axions can only arise near the boundary of the moduli space, the powerful results of asymptotic Hodge theory provide an ideal set of tools to draw general conclusions without the need to focus on specific geometric examples. We find that the boundary structure engraves a remarkable pattern in all possible scalar potentials generated by background fluxes. By studying the Newton polygons of the extremization conditions of all allowed scalar potentials and realizing the backreaction effects as Puiseux expansions, we find that this pattern forces a universal backreaction behavior of the large axion field on its saxion partner.


Author(s):  
Irina A. Antipova ◽  
Ekaterina A. Kleshkova ◽  
Vladimir R. Kulikov

In the paper, we deal with the problem of getting analytic continuations for the monomial function associated with a solution to the reduced trinomial algebraic system. In particular, we develop the idea of applying the Mellin-Barnes integral representation of the monomial function for solving the extension problem and demonstrate how to achieve the same result following the fact that the solution to the universal trinomial system is polyhomogeneous. As a main result, we construct Puiseux expansions (centred at the origin) representing analytic continuations of the monomial function


2017 ◽  
Vol 78 (1) ◽  
pp. 107-132 ◽  
Author(s):  
Tongke Wang ◽  
Yuesheng Gu ◽  
Zhiyue Zhang

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