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SMOOTH FANO 4-FOLDS IN GORENSTEIN FORMATS

Part of: Computational aspects in algebraic geometry Special varieties Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  31 May 2021

MUHAMMAD IMRAN QURESHI Open the ORCID record for MUHAMMAD IMRAN QURESHI [Opens in a new window]
MUHAMMAD IMRAN QURESHI*
Affiliation:
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
*
e-mail: imran.qureshi@kfupm.edu.sa
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Abstract

We construct some new deformation families of four-dimensional Fano manifolds of index one in some known classes of Gorenstein formats. These families have explicit descriptions in terms of equations, defining their image under the anticanonical embedding in some weighted projective space. They also have relatively smaller anticanonical degree than most other known families of smooth Fano 4-folds.

Keywords

Fano varietyGoresntein format4-fold

MSC classification

Primary: 14J45: Fano varieties
Secondary: 14J35: $4$-folds 14M07: Low codimension problems 14Q15: Higher-dimensional varieties
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 424 - 433
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

I would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum and Minerals for funding this work through the project No. SR191006.

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