Construction of Calabi-Yau -folds in

Author:
Fabio Tonoli

Journal:
J. Algebraic Geom. **13** (2004), 209-232

DOI:
https://doi.org/10.1090/S1056-3911-03-00371-0

Published electronically:
October 15, 2003

MathSciNet review:
2047696

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Abstract | References | Additional Information

Abstract: We give examples of smooth Calabi-Yau -folds in 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 .

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 -folds in .

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Additional Information

**Fabio Tonoli**

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

Email:
fabio.tonoli@uni-bayreuth.de

DOI:
https://doi.org/10.1090/S1056-3911-03-00371-0

Received by editor(s):
May 31, 2001

Published electronically:
October 15, 2003