145 research outputs found
On surfaces of general type with
The moduli space of surfaces of general type with (where is the genus of the Albanese fibration) was constructed by
Catanese and Ciliberto in \cite{CaCi93}. In this paper we characterize the
subvariety corresponding to surfaces
containing a genus 2 pencil, and moreover we show that there exists a
non-empty, dense subset which parametrizes
isomorphism classes of surfaces with birational bicanonical map.Comment: 35 pages. To appear in Collectanea Mathematic
Surfaces of general type with and bicanonical map of degree 2
We classify the minimal algebraic surfaces of general type with and bicanonical map of degree 2. It will turn out that they are
isogenous to a product of curves, so that if is such a surface then there
exist two smooth curves and a finite group acting freely on such that . We describe the and that
occur. In particular the curve is a hyperelliptic-bielliptic curve of genus
3, and the bicanonical map of is composed with the involution
induced on by , where is the hyperelliptic involution of . In this way we obtain
three families of surfaces with which yield the first known
examples of surfaces with these invariants. We compute their dimension, and we
show that they are three smooth and irreducible components of the moduli space
of surfaces with . For each of these families, an
alternative description as a double cover of the plane is also given, and the
index of the paracanonical system is computed.Comment: 36 pages. To appear in Transactions of the American Mathematical
Societ
Representations of braid groups and construction of projective surfaces
Braid groups are an important and flexible tool used in several areas of
science, such as Knot Theory (Alexander's theorem), Mathematical Physics
(Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this
note we will focus on their algebraic-geometric aspects, explaining how the
representation theory of higher genus braid groups can be used to produce
interesting examples of projective surfaces defined over the field of complex
numbers.Comment: Note written for the Proceedings of the Conference "Group 32 - The
32nd International Colloquium on Group Theoretical Methods in Physics", held
on Czech Technical University (Prague) on July 9-13, 201
On surfaces with p_g=q=2, K^2=5 and Albanese map of degree 3
We construct a connected, irreducible component of the moduli space of
minimal surfaces of general type with and , which contains
both examples given by Chen-Hacon and the first author. This component is
generically smooth of dimension 4, and all its points parametrize surfaces
whose Albanese map is a generically finite triple cover.Comment: 35 pages, 2 figures. Final version, to appear in the Osaka Journal of
Mathematic
A pair of rigid surfaces with and whose universal cover is not the bidisk
We construct two complex-conjugated rigid surfaces with and
whose universal cover is not biholomorphic to the bidisk. We show that these
are the unique surfaces with these invariants and Albanese map of degree ,
apart the family of product-quotient surfaces constructed by Penegini. This
completes the classification of surfaces with and Albanese map
of degree .Comment: Final version. To appear in IMR
On factoriality of threefolds with isolated singularities
We investigate the existence of complete intersection threefolds with only isolated, ordinary multiple points and we provide some
sufficient conditions for their factoriality.Comment: 18 pages. To appear in the Michigan Mathematical Journa
Finite quotients of surface braid groups and double Kodaira fibrations
Let be a closed Riemann surface of genus . We give an account
of some results obtained in the recent papers \cite{CaPol19, Pol20, PolSab21}
and concerning what we call here \emph{pure braid quotients},namely non-abelian
finite groups appearing as quotients of the pure braid group on two strands
. We also explain how these groups can be used in order
to provide new constructions of double Kodaira fibrations.Comment: 23 pages, 3 figures. To appear in "The Art of Doing Algebraic
Geometry", a Springer volume dedicated to Ciro Ciliberto. arXiv admin note:
text overlap with arXiv:2102.04963, arXiv:2002.01363, arXiv:1905.0317
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