|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Hodge theory of Calabi-Yau fibrations
If you have a question about this talk, please contact Burt Totaro.
Abstract: This talk is about 1-parameter families of elliptic curves, K3 surfaces, and Calabi-Yau 3-folds—objects which arise, for example, in the theory of modular forms and in mirror symmetry—with particular attention to the role played by singular fibers. Instead of looking at the geometry of the family directly, one often studies the associated “variation of Hodge [i.e., complex analytic] structure”, and the degrees of related vector bundles on the parameter space are a tool for studying global behavior.
In his classic study of minimal elliptic fibrations, Kodaira described all possible singular fibers and their relation to the A-D-E classification (from Lie/singularity theory). We will first recall this and how one can relate fiber types to the Euler characteristic of the total space and the degree of the Hodge bundles.
What is interesting is how these relations generalize (or fail to generalize) to higher dimensions (K3, CY 3 -fold), and the related nonexistence (or existence) of non-isotrivial families with no singular fibers. We will describe some results along these (global) lines; if time permits, we will sketch how they fit with our earlier classification of (local) degenerations of CY threefold VHS ’s related to mirror symmetry, and lead to a Torelli theorem for the mirror quintic family.
This talk is part of the Algebraic Geometry Seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsEmerge Cambridge Computer Laboratory Tech Talks Regional Zebrafish meeting
Other talksCreole Shadow Empire: Histories of Intimacy across Southeast Asia, 1850-1950 Travel writing A couple of efficient prediction models for underground railway-induced vibrations Design and Evolution of New Biocatalysts for Organic Synthesis Production Processes Group Seminar - TBC 'It's Not My Story to Tell': Ownership, Legitimacy, and the Politics of History in Mocimboa da Praia, Mozambique