Arithmetically Gorenstein Calabi--Yau threefolds in $\mathbb{P}^7$

Stephen  Coughlan; Łukasz  Gołębiowski; Grzegorz  Kapustka; Michał  Kapustka

doi:10.3934/era.2016.23.006

Article Contents

2016, Volume 23: 52-68. Doi: 10.3934/era.2016.23.006

This volume Previous Article Banach limit in convexity and geometric means for convex bodies Next Article

Arithmetically Gorenstein Calabi--Yau threefolds in $\mathbb{P}^7$

1.
Mathematisches Institut, Lehrstuhl Mathematik VIII, Universität Bayreuth, Universitätsstrasse 30, D-95447 Bayreuth
2.
Jagiellonian University Cracow
3.
Jagiellonian University Cracow, University of Zürich
4.
University of Stavanger, Department of Mathematics and Natural Sciences, NO-4036 Stavanger

Received: August 31, 2016

Revised: September 30, 2016

Published: December 2015

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Abstract

We present a list of arithmetically Gorenstein Calabi--Yau threefolds in $\mathbb{P}^7$ and give evidence that this is a complete list. In particular we construct three new families of arithmetically Gorenstein Calabi--Yau threefolds in $\mathbb{P}^7$ for which no mirror construction is known.

Keywords:

Calabi-Yau threefolds,
Gorenstein structure.

Mathematics Subject Classification: 14J32.

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