Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Construction of Calabi-Yau $3$-folds in $\mathbb P^6$

Author: Fabio Tonoli
Journal: J. Algebraic Geom. 13 (2004), 209-232
Published electronically: October 15, 2003
MathSciNet review: 2047696
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Abstract | References | Additional Information

Abstract: We give examples of smooth Calabi-Yau $3$-folds in $\mathbb P^6$ of low degree, up to the first difficult case, which occurs in degree 17. In this case we show the existence of three unirational components of their Hilbert scheme, all having the same dimension $23+48=71$.

The constructions are based on the Pfaffian complex, choosing an appropriate vector bundle starting from their cohomology table. This translates into studying the possible structures of their Hartshorne-Rao modules.

We also give a criterium to check the smoothness of $3$-folds in $\mathbb P^6$.

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Additional Information

Fabio Tonoli
Affiliation: Mathematisches Institut der Universität Bayreuth, Universitätstrasse, D-95440 Bayreuth Deutschland

Received by editor(s): May 31, 2001
Published electronically: October 15, 2003

American Mathematical Society