# Paola ComparinUniversidad de La Frontera · Department of Mathematics and Statistics

Paola Comparin

PhD in mathematics

## About

19

Publications

741

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

93

Citations

Introduction

Algebraic geometry:
- symplectic and non-symplectic automorphisms on K3 surfaces
- elliptic fibrations
- Berglund-Hübsch-Chiodo-Ruan mirror construction and mirror symmetry for K3 surfaces
- toric geometry and mirror constructions

**Skills and Expertise**

Additional affiliations

January 2020 - present

May 2018 - December 2019

November 2014 - May 2018

Education

September 2011 - September 2014

## Publications

Publications (19)

It was shown by Mukai that the maximum order of a finite group acting faithfully and symplectically on a K3 surface is 960 and if such a group has order 960, then it is isomorphic to the Mathieu group . In this paper, we are interested in projective K3 surfaces admitting a faithful symplectic action of the group . We show that there are infinitely...

H\"ohn and Mason classified the possible symplectic groups acting on an Irreducible Holomorphic Symplectic (IHS) manifold of K3$^{[2]}$-type, finding that $\mathbb Z_3^4 : \mathcal A_6$ is the symplectic group with the biggest order. In this paper, we study the possible IHS manifolds of K3$^{[2]}$-type with a symplectic action of $\mathbb Z_3^4 : \...

We consider K3 surfaces of Picard rank 14 which admit a purely non‐symplectic automorphism of order 16. The automorphism acts on the second cohomology group with integer coefficients and we compute the invariant sublattice for the action. We show that all of these K3 surfaces admit an elliptic fibration and we compute the invariant lattices in a ge...

In this paper we present a classification of non-symplectic automorphisms of K3 surfaces whose order is a multiple of seven by describing the topological type of their fixed locus. In the case of purely non-symplectic automorphisms, we provide new results for order 14 and alternative proofs for orders 21, 28 and 42. For each of these orders we also...

It was shown by Mukai that the maximum order of a finite group acting faithfully and symplectically on a K3 surface is 960 and if such a group has order 960, then it is isomorphic to the Mathieu group $M_{20}$. In this paper, we are interested in projective K3 surfaces admitting a faithful symplectic action of the group $M_{20}$. We show that there...

The moduli space of K3 surfaces X with a purely non-symplectic automorphism \sigma of order n\geq 2 is one dimensional exactly when \varphi(n)=8 or 10 . In this paper we classify and give explicit equations for the very general members (X,\sigma) of the irreducible components of maximal dimension of such moduli spaces. In particular, we show that t...

For certain K3 surfaces, there are two constructions of mirror symmetry that appear very different. The first, known as BHK mirror symmetry, comes from the Landau–Ginzburg model for the K3 surface; the other, known as LPK3 mirror symmetry, is based on a lattice polarization of the K3 surface in the sense of Dolgachev’s definition. There is a large...

The moduli space of K3 surfaces $X$ with a purely non-symplectic automorphism $\sigma$ of order $n\geq 2$ is one dimensional exactly when $\varphi(n)=8$ or $10$. In this paper we classify and give explicit equations for the very general members $(X,\sigma)$ of the irreducible components of maximal dimension of such moduli spaces. In particular we s...

In this paper, we provide a complete classification of non-symplectic automorphisms of order 9 of complex K3 surfaces.

We consider K3 surfaces of Picard rank 14 which admit a purely nonsymplectic automorphism of order 16. The automorphism acts on the second cohomology group with integer coefficients and we compute the invariant sublattice for the action. We show that all of these K3 surfaces admit an elliptic fibration and we compute the invariant lattices in a geo...

In this paper we provide a complete classification of non-symplectic automorphisms of order nine of complex K3 surfaces.

For certain K3 surfaces, there are two constructions of mirror symmetry that are very different. The first, known as BHK mirror symmetry, comes from the Landau-Ginzburg model for the K3 surface; the other, known as LPK3 mirror symmetry, is based on a lattice polarization of the K3 surface in the sense of Dolgachev's definition. There is a large cla...

We provide a combinatorial characterization of monomial linear systems on toric varieties whose general member is quasismooth. This is given both in terms of the Newton polytope and in terms of the matrix of exponents of a monomial basis.

In this paper we consider the class of K3 surfaces defined as hypersurfaces in weighted projective space, and admitting a non-symplectic automorphism of non-prime order, excluding the orders 4, 8, and 12. We show that on these surfaces the Berglund-H\"ubsch-Krawitz mirror construction and mirror symmetry for lattice polarized K3 surfaces constructe...

We provide a sufficient condition for a general hypersurface in a $\mathbb
Q$-Fano toric variety to be a Calabi-Yau variety in terms of its Newton
polytope. Moreover, we define a generalization of the Berglund-H\"ubsch-Krawitz
construction in case the ambient is a $\mathbb Q$-Fano toric variety with
torsion free class group and the defining polynom...

We consider K3 surfaces that possess certain automorphisms of prime order p>2
and we present, for these surfaces, a correspondence between the mirror
symmetry of Berglund-Huebsch-Chiodo-Ruan and that for lattice polarized K3
surfaces presented by Dolgachev.

In this paper we classify the elliptic fibrations on K3 surfaces which are
the double cover of a blow up of $\mathbb{P}^2$ branched along rational curves
and we give equations for many of these elliptic fibrations. Thus we obtain a
classification of the van Geemen--Sarti involutions (which are symplectic
involutions induced by a translation by a 2-...