A Construction of Frobenius Manifolds with Logarithmic Poles and Applications
A Construction of Frobenius Manifolds with Logarithmic Poles and Applications
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具有对数极点的弗罗贝尼乌斯流形的构造及应用
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发表时间：
2008
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通讯作者：
Thomas Reichelt
中科院分区：
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作者：
Thomas Reichelt
建立了具有对数极点的Frobenius流形的一个构造定理。这是赫特灵和马宁的一个定理的推广。作为应用，我们证明了Kontsevich和Manin关于具有收敛Gromov-Witten势的射影光滑簇的重构定理的部分推广。第二个应用是从极化霍奇结构的变体中构造Frobenius流形，当满足某些生成条件时，该结构沿法向交叉因子退化。
A construction theorem for Frobenius manifolds with logarithmic poles is established. This is a generalization of a theorem of Hertling and Manin. As an application we prove a partial generalization of the reconstruction theorem of Kontsevich and Manin for projective smooth varieties with convergent Gromov-Witten potential. A second application is a construction of Frobenius manifolds out of a variation of polarized Hodge structures which degenerates along a normal crossing divisor when certain generation conditions are fulfilled.