共查询到20条相似文献,搜索用时 10 毫秒
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Ying Chen 《Central European Journal of Mathematics》2014,12(1):28-38
We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial f: ?2n → ?2. By using strongly non-degenerate condition, we prove a counterpart of Némethi and Zaharia’s fibration theorem. In particular, we obtain a global version of Oka’s fibration theorem for strongly non-degenerate and convenient mixed polynomials. 相似文献
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We first define the notion of the infimum at infinity of a polynomial function and the notion of stability at infinity near the fiber of the gradient descent system. Then we prove that the gradient descent system is stable at infinity near the fiber of the infimum value at infinity. 相似文献
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Jens Piontkowski 《manuscripta mathematica》2001,106(1):75-99
A projective variety is called developable if the image of its Gauss map has a smaller dimension than the variety itself.
Developable varieties are always singular, and requiring that all singularities lie in a hyperplane puts a severe restriction
on them. Here we refine a theorem of Wu and Zheng stating that such varieties are the union of cones if the dimension of the
Gauss image is less than or equal to four. Afterwards we study their singular locus. Finally, we describe the geometry of
such varieties whose Gauss image has dimension two.
Received: Received: 8 November 2000 / Revised version: 15 May 2001 相似文献
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In this paper we define the relation of analytic equivalence of functions at infinity. We prove that if the ?ojasiewicz exponent at infinity of the gradient of a polynomial f∈R[x1,…,xn] is greater or equal to k−1, then there exists ε>0 such that for every polynomial P∈R[x1,…,xn] of degree less or equal to k, whose coefficients of monomials of degree k are less or equal ε, the polynomials f and f+P are analytically equivalent at infinity. 相似文献
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Miran Černe 《Arkiv f?r Matematik》2002,40(1):27-45
LetX(-ϱB
m
×C
n
be a compact set over the unit sphere ϱB
m
such that for eachz∈ϱB
m
the fiberX
z
={ω∈C
n
;(z, ω)∈X} is the closure of a completely circled pseudoconvex domain inC
n
. The polynomial hull
ofX is described in terms of the Perron-Bremermann function for the homogeneous defining function ofX. Moreover, for each point (z
0,w
0)∈Int
there exists a smooth up to the boundary analytic discF:Δ→B
m
×C
n
with the boundary inX such thatF(0)=(z
0,w
0).
This work was supported in part by a grant from the Ministry of Science of the Republic of Slovenia. 相似文献
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A. S. Pyartli 《Proceedings of the Steklov Institute of Mathematics》2006,254(1):121-151
Quadratic vector fields for which the line at infinity is a phase curve with three different singular points are considered. It is assumed that the characteristic numbers of these singular points are not multiples of 1/4 or 1/6. It is shown that among the fields with fixed characteristic numbers satisfying this assumption, one can choose seven fields such that any other field with solvable noncommutative monodromy group at infinity is affine equivalent to one of the chosen fields. In addition, quadratic vector fields with commutative monodromy group at infinity are described. 相似文献
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Michela Artebani Gian Pietro Pirola 《Proceedings of the American Mathematical Society》2005,133(2):331-341
Let be a compact Riemann surface of genus and be an integer. We show that admits meromorphic functions with monodromy group equal to the alternating group
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A. N. Kirillov 《Journal of Mathematical Sciences》1984,25(2):1051-1057
The results of A. N. Varchenko regarding the zeta-function of the monodromy operator for a singular point of a hypersurface are generalized to the case of a complete intersection singularity.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 112–120, 1981. 相似文献