1. CJM Online first
 Shimada, Ichiro

On an Enriques surface associated with a quartic Hessian surface
Let $Y$ be a complex Enriques surface
whose universal cover $X$ is birational to a general quartic
Hessian surface.
Using the result on the automorphism group of $X$
due to Dolgachev and Keum,
we obtain
a finite presentation of the automorphism group of $Y$.
The list of elliptic fibrations on $Y$
and the list of combinations of rational double points that can
appear on a surface birational to $Y$
are presented.
As an application,
a set of generators of
the automorphism group of the generic Enriques surface is calculated
explicitly.
Keywords:Enriques surface, K3 surface, automorphism, lattice Categories:14J28, 14Q10 

2. CJM 2017 (vol 70 pp. 702)
 Xia, Eugene Z.

The Algebraic de Rham Cohomology of Representation Varieties
The $\operatorname{SL}(2,\mathbb C)$representation varieties of punctured surfaces
form natural families parameterized by monodromies at the punctures.
In this paper, we compute the loci where these varieties are
singular for the cases of oneholed and twoholed tori and the
fourholed sphere. We then compute the de Rham cohomologies
of these varieties of the oneholed torus and the fourholed
sphere when the varieties are smooth via the Grothendieck theorem.
Furthermore, we produce the explicit GaussManin connection
on the natural family of the smooth $\operatorname{SL}(2,\mathbb C)$representation
varieties of the oneholed torus.
Keywords:surface, algebraic group, representation variety, de Rham cohomology Categories:14H10, 13D03, 14F40, 14H24, 14Q10, 14R20 

3. CJM 2012 (vol 65 pp. 961)
 Aholt, Chris; Sturmfels, Bernd; Thomas, Rekha

A Hilbert Scheme in Computer Vision
Multiview geometry is the study of
twodimensional images of threedimensional scenes, a foundational subject in computer vision.
We determine a universal GrÃ¶bner basis for the multiview ideal of $n$ generic cameras.
As the cameras move, the multiview varieties vary in a family of dimension $11n15$.
This family is the distinguished component of a multigraded Hilbert scheme
with a unique Borelfixed point.
We present a combinatorial study
of ideals lying on that Hilbert scheme.
Keywords:multigraded Hilbert Scheme, computer vision, monomial ideal, Groebner basis, generic initial ideal Categories:14N, 14Q, 68 

4. 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 
