Some Enumerative Global Properties of Variations of Hodge Structures
نویسندگان
چکیده
The global enumerative invariants of a variation of polarized Hodge structures over a smooth quasi-projective curve reflect the global twisting of the family and numerical measures of the complexity of the limiting mixed Hodge structures that arise when the family degenerates. We study several of these global enumerative invariants and give applications to questions such as: Give conditions under which a non-isotrivial family of Calabi-Yau threefolds must have singular fibres? Determine the correction terms arising from the limiting mixed Hodge structures that are required to turn the classical Arakelov inequalities into exact equalities. Outline
منابع مشابه
Introduction to Variations of Hodge Structure Summer School on Hodge Theory, Ictp, June 2010
These notes are intended to accompany the course Introduction to Variations of Hodge Structure (VHS) at the 2010 ICTP Summer School on Hodge Theory. The modern theory of variations of Hodge structure (although some authors have referred to this period as the pre-history) begins with the work of Griffiths [23, 24, 25] and continues with that of Deligne [17, 18, 19], and Schmid [41]. The basic ob...
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It’s well known that multiple polylogarithms give rise to good unipotent variations of mixed Hodge-Tate structures. In this paper we shall explicitly determine these structures related to multiple logarithms and some other multiple polylogarithms of lower weights. The purpose of this explicit construction is to give some important applications: First we study of the limit mixed Hodge-Tate struc...
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