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Calabi-Yau fourfolds in products of projective space. (English) Zbl 1325.14058
Donagi, Ron (ed.) et al., String-Math 2013. Selected papers based on the presentations at the conference, Stony Brook, NY, USA, June 17–21, 2013. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1051-3/hbk; 978-1-4704-1999-8/ebook). Proceedings of Symposia in Pure Mathematics 88, 281-290 (2014).
Summary: We report on recent work classifying all Calabi-Yau fourfolds which can be described as complete intersections in products of projective space. In addition to providing a finite list of configuration matrices which can describe all families of such manifolds, we give information on some of their simple geometrical properties. This includes their Chern classes, Hodge data and some elliptic fibration structures. Throughout we illustrate the computations and description of these manifolds with the aid of a concrete example.
This work is motivated by a desire to make use of this explicit class of fourfolds in the physical context of F-theory compactification. Similar work involving analgous threefolds has played an important role in the heterotic string theory literature.
For the entire collection see [Zbl 1304.14003].

##### MSC:
 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 14J35 $$4$$-folds
##### Keywords:
Calabi-Yau; algebraic geometry