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Title: An introduction to Hodge structures
Authors: Filippini, Sara Angela
Ruddat, Helge
Thompson, Alan
Issue Date: 2015
Publisher: © Springer
Citation: FILIPPINI, S.A., RUDDAT, H. and THOMPSON, A., 2015. An Introduction to Hodge Structures. IN: Laza, R., Schutt, M. and Yui, N. (eds.) Calabi-Yau Varieties: Arithmetic, Geometry and Physics. Lecture Notes on Concentrated Graduate Courses. New York: Springer, pp. 83-130.
Series/Report no.: Fields Institute Monographs;34
Abstract: We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kahler manifolds to the families of Hodge structures defined on their cohomology, and discuss its properties. This will lead us to the more general definition of a variation of Hodge structure and the Gauss-Manin connection. We then review the basics about mixed Hodge structures with a view towards degenerations of Hodge structures; including the canonical extension of a vector bundle with connection, Schmid's limiting mixed Hodge structure and Steenbrink's work in the geometric setting. Finally, we give an outlook about Hodge theory in the Gross-Siebert program.
Description: This book chapter is in closed access.
Sponsor: A. Thompson was supported by a Fields-Ontario-PIMS postdoctoral fellowship with funding provided by NSERC, the Ontario Ministry of Training, Colleges and Universities, and an Alberta Advanced Education and Technology Grant.
Version: Accepted for publication
DOI: 10.1007/978-1-4939-2830-9_4
URI: https://dspace.lboro.ac.uk/2134/35220
Publisher Link: https://doi.org/10.1007/978-1-4939-2830-9_4
ISBN: 9781493928293
9781493928309
ISSN: 1069-5273
Appears in Collections:Closed Access (Maths)

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