My area of interest is singularity theory, and in particular hyperplane arrangements. I am interested in understanding the links between the topological, algebraic and combinatorial aspects of these objects.

A Weyl arrangement is the hyperplane arrangement defined by a root system.
Arnold and Saito proved that every Weyl arrangement is free. The Weyl
subarrangements of type are represented by simple graphs. Stanley
gave a characterization o...

A -tuple total dominating set (TDS) of a graph is a set of
vertices in which every vertex in is adjacent to at least vertices in
. The minimum size of a TDS is called the -tuple total dominating
number and it is deno...

Every subarrangement of Weyl arrangements of type is represented
by a signed graph. Edelman and Reiner characterized freeness of subarrangements
between type and type in terms of graphs. Recently,
Suyama an...

We introduce the package \textbf{arrangements} for the software CoCoA. This
package provides a data structure and the necessary methods for working with
hyperplane arrangements. In particular, the package implements methods to
enumerate many commo...

Anna Maria Bigatti, Elisa Palezzato, Michele Torielli

Journal of Algebra and its Applications Apr 2018 [Refereed]

In this paper we want to revive the object sectional matrix which encodes the
Hilbert functions of successive hyperplane sections of a homogeneous ideal. We
translate and/or reprove recent results in this language. Moreover, some new
results are s...

In this paper, we study the class of free hyperplane arrangements.
Specifically, we investigate the relations between freeness over a field of
finite characteristic and freeness over .

Graphs and Combinatorics 34(3) 477-488 Mar 2018 [Refereed]

The fundamental group of the complement of a hyperplane arrangement in a
complex vector space is an important topological invariant. The third rank of
successive quotients in the lower central series of the fundamental group was
called Falk invari...

Anna Maria Bigatti, Elisa Palezzato, Michele Torielli

Journal of Algebraic Combinatorics Sep 2018

In this article we describe two new characterizations of freeness for
hyperplane arrangements via the study of the generic initial ideal and of the
sectional matrix of the Jacobian ideal of arrangements.

Two new characterizations of free hyperplane arrangements

Anna Maria Bigatti, Elisa Palezzato, Michele Torielli

Monografıas de la Real Academia de Ciencias. Zaragoza 43 59-62 2018 [Refereed]

The fundamental group of the complement of a hyperplane arrangement in a
complex vector space is an important topological invariant. The third rank of
successive quotients in the lower central series of the fundamental group was
called Falk invari...

In this paper we give a very natural description of the bijections between
the minimal CW-complex homotopy equivalent to the complement of a supersolvable
arrangement , the basis of the Orlik-Solomon
algebra associated ...

The resonant band is a useful notion for the computation of the nontrivial
monodromy eigenspaces of the Milnor fiber of a real line arrangement. In this
article, we develop the resonant band description for the cohomology of the
Aomoto complex. As...

Topology and its Applications 178 288-299 Nov 2013

A rank one local system on the complement of a hyperplane arrangement is said
to be admissible if it satisfies certain non-positivity condition at every
resonant edges. It is known that the cohomology of admissible local system can
be computed com...

Ann. Inst. Fourier (Grenoble), vol. 63 (2013) 63(6) 2097-2136 Oct 2011

We investigate deformations of free and linear free divisors. We introduce a
complex similar to the de Rham complex whose cohomology calculates deformation
spaces. This cohomology turns out to be zero for many linear free divisors and
to be constr...