arXiv subjects
Publications and source records attributed to Letizia Pernigotti.
The global geometry of the moduli spaces of higher spin curves and their birational classification is largely unknown for g >= 2 and r > 2. Using quite related geometric constructions, we almost complete the picture of the known results in genus g <= 4 showing the rationality of the moduli spaces of even and odd 4-spin curves of genus 3, of odd spin curves of genus 4 and of 3-spin curves of genus 4.
We study the surjectivity of suitable weighted Gaussian maps which provide a natural generalization of the standard Gaussian maps and encode the local geometry of the locus of curves endowed with a higher root of the canonical bundle having associated linear system of dimension at least r + 1. In particular, we get a bound on the dimension of its Zariski tangent space, which turns out to be sharp in the special case r = 0. Finally, we describe this locus in the case of complete intersection curves.
We refine the notion of higher spin curves defined in terms of line bundles by Caporaso, Cornalba and Casagrande by adding the data of coherent nets of roots introduced by Jarvis in terms of torsion-free sheaves and we describe the boundary part of their moduli space. We provide then a presentation of the rational Picard group of this moduli space.
Shape matching represents a challenging problem in both information engineering and computer science, exhibiting not only a wide spectrum of multimedia applications, but also a deep relation with conformal geometry. After reviewing the theoretical foundations and the practical issues involved in this fashinating subject, we focus on two state-of-the-art approaches relying respectively on local features (landmark points) and on global properties (conformal parameterizations). Finally, we introduce the Teichmüller space of n-pointed Riemann surfaces of genus g into the realm of multimedia, showing that its beautiful geometry provides a natural unified framework for three-dimensional shape matching.