Linear free divisors and Frobenius manifolds

被引：16
作者：
de Gregorio, Ignacio [1 ]
Mond, David [1 ]
Sevenheck, Christian [2 ]
机构：
[1] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England
[2] Univ Mannheim, Lehrstuhl Math 6, D-68131 Mannheim, Germany
来源：
COMPOSITIO MATHEMATICA | 2009年 / 145卷 / 05期
基金：
英国工程与自然科学研究理事会;
关键词：
linear free divisors; prehomogenous vector spaces; quiver representations; Gauss-Manin system; Brieskorn lattice; Birkhoff problem; spectral numbers; Frobenius manifolds; QUANTUM COHOMOLOGY;
D O I：
10.1112/S0010437X09004217
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study linear functions on fibrations whose central fibre is a linear free divisor. We analyse the GauB-Manin system associated to these functions, and prove the existence of a primitive and homogenous form. As a consequence, we show that the base space of the semi-universal unfolding of such a function carries a Frobenius manifold structure.
引用
收藏
页码：1305 / 1350
页数：46
相关论文
共 37 条
[1]  
[Anonymous], 1998, Progr. Math., V160, P141
[2]   MILNOR NUMBERS AND THE TOPOLOGY OF POLYNOMIAL HYPERSURFACES [J].
BROUGHTON, SA .
INVENTIONES MATHEMATICAE, 1988, 92 (02) :217-241
[3]  
BUCHWEITZ RO, 2006, LONDON MATH SOC LECT, V324, P41
[4]   The quantum orbifold cohomology of weighted projective spaces [J].
Coates, Tom ;
Corti, Alessio ;
Lee, Yuan-Pin ;
Tseng, Hsian-Hua .
ACTA MATHEMATICA, 2009, 202 (02) :139-193
[5]   On the legacy of free divisors III: Functions and divisors on complete intersections [J].
Damon, J .
QUARTERLY JOURNAL OF MATHEMATICS, 2006, 57 :49-79
[6]   Some examples of non-massive Frobenius manifolds in singularity theory [J].
de Gregorio, Ignacio .
JOURNAL OF GEOMETRY AND PHYSICS, 2007, 57 (09) :1829-1841
[7]   Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I) [J].
Douai, A ;
Sabbah, C .
ANNALES DE L INSTITUT FOURIER, 2003, 53 (04) :1055-+
[8]  
DOUAI A, 2008, MATHAG08062011
[9]  
Douai Antoine, 2004, ASPECTS MATH E, V36, P1
[10]  
GIVENTAL AB, 1995, P INT C MATH ZUR 199, V1, P472
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