Gorenstein formats, canonical and Calabi-Yau threefolds
Gavin Brown, Alexander Kasprzyk, Lei Zhu
TL;DR
This paper extends the classification of threefolds, including Calabi-Yau varieties with singularities, using Gorenstein formats to construct and analyze various classes of complex algebraic threefolds beyond complete intersections.
Contribution
It introduces new classes of threefolds, including non-complete intersections and Calabi-Yau varieties with singularities, using Gorenstein formats for construction and classification.
Findings
Extended classification of threefolds of general type
Constructed Calabi-Yau threefolds with canonical singularities
Applied Gorenstein formats to describe orbifolds
Abstract
We extend the known classification of threefolds of general type that are complete intersections to various classes of non-complete intersections, and find other classes of polarised varieties, including Calabi-Yau threefolds with canonical singularities, that are not complete intersections. Our methods apply more generally to construct orbifolds described by equations in given Gorenstein formats.
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