Caporaso, Lucia Melo, Margarida Pacini, Marco
Published in
Selecta Mathematica

We study the tropicalization of the moduli space of algebraic spin curves, S¯g,n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{\mathcal {S}}_{g,n}$$\end{docu...

Holmes, David Kass, Jesse Leo Pagani, Nicola
Published in
European Journal of Mathematics

We prove that the extension of the double ramification cycle defined by the first-named author (using modifications of the stack of stable curves) coincides with one of those defined by the last-two named authors (using an extended Brill–Noether locus on a suitable compactified universal Jacobians). In particular, in the untwisted case we deduce th...

Carocca, Angel Lange, Herbert Rodríguez, Rubí E.
Published in
Archiv der Mathematik

An automorphism of an abelian variety induces a decomposition of the variety up to isogeny. There are two such results, namely the isotypical decomposition and Roan’s decomposition theorem. We show that they are essentially the same. Moreover, we generalize in a sense this result to abelian varieties with action of an arbitrary finite abelian group...

Kummer, Mario
Published in
Annali di Matematica Pura ed Applicata (1923 -)

A totally real theta characteristic of a real curve is a theta characteristic which is linearly equivalent to a sum of only real points. These are closely related to the facets of the convex hull of the canonical embedding of the curve. We give upper and lower bounds for the number of both of totally real theta characteristics and facets.

Wei, Fu-Tsun Yamazaki, Takao
Published in
Forum Mathematicum

We consider the generalized Jacobian J ~ {\widetilde{J}} of the modular curve X 0 ( N ) {X_{0}(N)} of level N with respect to a reduced divisor consisting of all cusps. Supposing N is square free, we explicitly determine the structure of the ℚ {\mathbb{Q}} -rational torsion points on J ~ {\widetilde{J}} up to 6-primary torsion. The result depicts...

Li, Wanlin Mantovan, Elena Pries, Rachel Tang, Yunqing
Published in
Research in Number Theory

By a result of Moonen, there are exactly 20 positive-dimensional families of cyclic covers of the projective line for which the Torelli image is open and dense in the associated Shimura variety. For each of these, we compute the Newton polygons, and the μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \...

Borówka, Paweł Ortega, Angela
Published in
Mathematische Zeitschrift

We investigate the number and the geometry of smooth hyperelliptic curves on a general complex abelian surface. We give a short proof for the known fact the only possibilities of genera of such curves are 2, 3, 4 and 5; then we focus on the genus five case. We prove that up to translation, there is a unique hyperelliptic curve in the linear system ...

Ghigi, Alessandro
Published in
Bollettino dell'Unione Matematica Italiana

In this note we survey recent results on the extrinsic geometry of the Jacobian locus inside Ag\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {A}_g$$\end{docum...

Lange, Herbert Ortega, Angela
Published in
Archiv der Mathematik

We work out the cases in which the Prym map is dominant and generically finite for étale or totally ramified cyclic coverings.

Komeda, Jiryo Matsutani, Shigeki Previato, Emma
Published in
Letters in Mathematical Physics

A recent generalization of the “Kleinian sigma function” involves the choice of a point P of a Riemann surface X, namely a “pointed curve” (X, P). This paper concludes our explicit calculation of the sigma function for curves cyclic trigonal at P. We exhibit the Riemann constant for a Weierstrass semigroup at P with minimal set of generators {3,2r+...