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arXiv · 2010.03086

The Monodromy problem for hyperelliptic curves

Daniel López Garcia
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Abstract

We study the Dynkin diagram associated to the monodromy of direct sums of polynomials. The monodromy problem asks under which conditions on a polynomial, the monodromy of a vanishing cycle generates the whole homology of a regular fiber. We consider the case $y^4+g(x)$, which is a generalization of the results of Christopher and Marde$\check{s}$i\'c about the monodromy problem for hyperelliptic curves. Moreover, We solve the monodromy problem for direct sums of fourth degree polynomials.

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Daniel López Garcia. 2020-10-06. The Monodromy problem for hyperelliptic curves. https://arxiv.org/abs/2010.03086

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