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Trudy MIRAN, vyp.238. Monodromiya v zadachah algebraicheskoj geometrii i differencial'nyh uravnenij (Nauka, 2002)(ISBN 5020064246)(ru)(600dpi)(T)(224s).djvu |
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Size 3.3Mb Date Feb 18, 2005 |
isomorphism, we say that the logarithmic comparison theorem holds for D (or, simply, LCT holds
for D)...
The kernel К of фр is supported by the origin
(because / is smooth outside @,0)), and CCh(Mlog) = CCh(ii:) + CCh(O[*D})...
^
First, it is necessary to consider a free resolution of MlogD analogous to the resolution of Mlog
(see Theorem 4.3)...
We have used [10, 12] and
[16] again to compute the Ь-function and the annihilating ideal of 1//, that is to say, the algorithms
of [14]...
Prom the topological properties of / we can extract the following data:
(i) the topology of the special fibers /"^(s), s G Bf, and the inclusion of any special fiber f~1(s)
in its "tube" f~1(Ds), where Ds is a sufficiently small disc centered at s;
(ii) the topology of the generic fiber F := /-1E) for s £ Bf;
(iii) the monodromy representation of the function / (with integer or complex coefficients):
pf: 7ri(C\£/,pt) -> Aut(tf*(F))...
The goal of our paper is to study the behavior of data (i)-(iii) with respect to the Thom-
Sebastiani construction...
Nevertheless, in Theorem 4.7, a join decomposition
is obtained under some additional conditions...
Fix a star for Bf as above and set mi = Pfjkir/%) and mi — P/,fcGi)- Let Si be the span of all
vectors mi(c) -c, where с G Hk(¥)...
In the first part, we discuss the compatibility of decomposition 2.3 with the Thom-Sebastiani
construction...
DIMCA, NEMETHI
(ii) the above decomposition is compatible with the inclusion Щ <—)> h~1(Do): realize the
space Щ as
C1 xGJIFxGJIFxC1'
FxG FxG
(where the maps are induced by the natural inclusions) and embed Щ in the tube h~l(D$) by the
map induced by the five natural inclusions С1 х G —> О1 х G, FxG—> f~1(Di) x G, etc...
The class С is well suited for our study, since if two polynomials / and g satisfy C\ and/or C2,
the same is true for their sum h = / 0 g...
On the other hand, the bifurcation set Bf = {b\,..., bt} can be a rich set and the corresponding
monodromy representation pf can be very complicated...
(ii) For any 1 < j < t, set rrij = pf(jj): 0*=i #*,* -> 0*=i I
position as it is described in Subsection 2.5...
Similarly, s is the boundary of Cone(s) that stays above the union of pr2prf J(image(r)) and
a small disc centered at 0...
In fact, for t = 2, the list of all rigid passports is known (see [13], where the result is attributed
to N.M...
Now, one can verify that F has a projective model F that is an elliptic curve and is the generic
fiber of an elliptic fibration whose special fiber at bi is of type II in the Kodaira classification (see [9]
for more details)...
Они полностью опре-
определяются алгеброй Ли симметрии модели и некоторым комплексным параметром...
Главными ин-
ингредиентами соответствующей теории являются следующие алгебраические объекты и факты...
], и задается
представленными ниже явными формулами (см...
Ниже рассматриваются
деформации, в которых число параметров не превосходит числа г различных длин корней
исходной алгебры Ли, а соответствующие формальные параметры обозначаются /ii,...,/ir,
г = 1,2...
Краткое описание геометрического метода получения аксиом для структурных элемен-
элементов сплетенной квазибиалгебры типа Вп...
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