1. CJM 2011 (vol 63 pp. 616)
 Lee, Edward

A Modular Quintic CalabiYau Threefold of Level 55
In this note we search the parameter space of HorrocksMumford quintic
threefolds and locate a CalabiYau threefold that is modular, in the
sense that the $L$function of its middledimensional cohomology is
associated with a classical modular form of weight 4 and level 55.
Keywords: CalabiYau threefold, nonrigid CalabiYau threefold, twodimensional Galois representation, modular variety, HorrocksMumford vector bundle Categories:14J15, 11F23, 14J32, 11G40 

2. CJM 2009 (vol 61 pp. 1050)
 Bertin, MarieAmélie

Examples of CalabiYau 3Folds of $\mathbb{P}^{7}$ with $\rho=1$
We give some examples of CalabiYau $3$folds with $\rho=1$ and
$\rho=2$, defined over $\mathbb{Q}$ and constructed as
$4$codimensional subvarieties of $\mathbb{P}^7$ via commutative
algebra methods. We explain how to deduce their Hodge diamond and
top Chern classes from computer based computations over some
finite field $\mathbb{F}_{p}$. Three of our examples (of degree
$17$ and $20$) are new. The two others (degree $15$ and $18$) are
known, and we recover their wellknown invariants with our
method. These examples are built out of GulliksenNeg{\aa}rd and
KustinMiller complexes of locally free sheaves.
Finally, we give two new examples of CalabiYau $3$folds of
$\mathbb{P}^6$ of degree $14$ and $15$ (defined over
$\mathbb{Q}$). We show that they are not deformation equivalent to
Tonoli's examples of the same degree, despite the fact that they
have the same invariants $(H^3,c_2\cdot H, c_3)$ and $\rho=1$.
Categories:14J32, 14Q15 
