Construction of CalabiYau $3$folds in $\mathbb P^6$
Author:
Fabio Tonoli
Journal:
J. Algebraic Geom. 13 (2004), 209232
DOI:
https://doi.org/10.1090/S1056391103003710
Published electronically:
October 15, 2003
MathSciNet review:
2047696
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Abstract  References  Additional Information
Abstract: We give examples of smooth CalabiYau $3$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 HartshorneRao 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, D95440 Bayreuth Deutschland
Email:
fabio.tonoli@unibayreuth.de
Received by editor(s):
May 31, 2001
Published electronically:
October 15, 2003