Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

On the automorphisms of moduli spaces of curves

In the last years the biregular automorphisms of the Deligne-Mumford's and Hassett's compactifications of the moduli space of n-pointed genus g smooth curves have been extensively studied by A. Bruno and the authors. In this paper we give a survey of these recent results and extend our techniques to some moduli spaces appearing as intermediate steps of the Kapranov's and Keel's realizations of $\bar{M}_{0,n}$, and to the degenerations of Hassett's spaces obtained by allowing zero weights.Comment: 15 pages. The material of version 1 has been reorganized and expanded in this paper and in arXiv:1307.6828 on automorphisms of Hassett's moduli space

Conjugacy in the discretized fold bifurcation

AbstractIn this paper, we construct a conjugacy between the time-1-map of the solution flow generated by an ordinary differential equation and its numerical approximation in a neighborhood of a fold bifurcation point. Our main result is that the conjugacy is O(hp)-close to the identity on the center manifold where h is the step size and p is the order of the numerical method

Technology in Practice. A Library in Your Pocket

The article discusses the development of library Web pages designed for viewing on mobile devices and cell phones. The use of smartphones and cell phones to access internet content, library services that can be made accessible through the mobile Web, and population assessment options for libraries developing mobile Web sites are examined. Services designed for mobile use including reference services, library instruction, and catalog access are also discussed

Technology in Practice. Click Here to Engage

The article presents discussion of applied librarianship with technology. Particular attention is given to ways in which librarians offering instruction session can utilize communication and presentation technology to best reach as many patrons as possible. Details are given highlighting the interest which patrons exhibit to novel technology tools, ways of using technology to foster communication with different personalities, and using the social media platform Twitter

Technology in Practice. Information Literacy 2.0

In this article the author discusses critical inquiry and information literacy instruction in light of changes in information dissemination due to digital technology and social media. She emphasizes the impact of such changes for libraries and librarians, addressing information searching skills, networking skills, and professional development for librarians

Technology in Practice. Nurturing Innovation: Tips for managers and administrators

The article focuses on how library managers and administrators can encourage innovation in libraries and prevent the failure of new library services. The author suggests that managers should encourage staff to learn about new trends in technology, give staff time to experiment with new initiatives, and develop a work culture that is tolerant of risks. Other topics include budget cuts to libraries, patron population, and rate of return (ROI) for libraries