In response to the article by Ivan Kausz: A discriminant and an upper bound for w 2 for hyperelliptic arithmetic surfaces |
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Authors: | Ivan Kausz |
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Affiliation: | (1) Mathematisches Institut der Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany. E-mail |
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Abstract: | We define a natural discriminant for a hyperelliptic curve X of genus g over a field K as a canonical element of the (8g+4)th tensor power of the maximal exterior product of the vectorspace of global differential forms on X. If v is a discrete valuation on K and X has semistable reduction at v, we compute the order of vanishing of the discriminant at v in terms of the geometry of the reduction of X over v. As an application, we find an upper bound for the Arakelov self-intersection of the relative dualizing sheaf on a semistable hyperelliptic arithmetic surface. |
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Keywords: | hyperelliptic curves arithmetic surfaces Arakelov theory. |
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