p-Buchsbaum rank 2 bundles on the projective space

It has been proved by various authors that a normalized, 1-Buchsbaum rank 2 vector bundle on P3 is a nullcorrelation bundle, while a normalized, 2-Buchsbaum rank 2 vector bundle on P3 is an instanton bundle of charge 2. We find that the same is not true for 3-Buchsbaum rank 2 vector bundles on P3, and propose a conjecture regarding the classification of such objects.Comment: Corrected previous result

Uniform Steiner bundles

In this work we study $k$-type uniform Steiner bundles, being $k$ the lowest degree of the splitting. We prove sharp upper and lower bounds for the rank in the case $k=1$ and moreover we give families of examples for every allowed possible rank and explain which relation exists between the families. After dealing with the case $k$ in general, we conjecture that every $k$-type uniform Steiner bundle is obtained through the proposed construction technique.Comment: 23 pages, to appear at Annales de l'Institut Fourie

Moduli of autodual instanton bundles

We provide a description of the moduli space of framed autodual instanton bundles on projective space, focusing on the particular cases of symplectic and orthogonal instantons. Our description will use the generalized ADHM equations which define framed instanton sheaves.Comment: 20 page

The Poet in the Mirror: Epic and Autobiography in Dante’s Inferno

Simone Marchesi is Assistant Professor of French and Italian at Princeton University. This talk was delivered at Sacred Heart University on April 7, 2006, as part of the College of Arts & Sciences Lecture Series on “The Real and Fabled Worlds of Dante Alighieri.” All English translations in the text from Dante’s Divine Comedy are by Robert Hollander and Jean Hollander, in their edition published by Doubleday/Anchor in 2000

Curves with Canonical Models on Scrolls

Let $C$ be an integral and projective curve whose canonical model $C'$ lies on a rational normal scroll $S$ of dimension $n$. We mainly study some properties on $C$, such as gonality and the kind of singularities, in the case where $n=2$ and $C$ is non-Gorenstein, and in the case where $n=3$, the scroll $S$ is smooth, and $C'$ is a local complete intersection inside $S$. We also prove that a rational monomial curve with just one singular point lies on a surface scroll if and only if its gonality is at most $3$, and that it lies on a threefold scroll if and only if its gonality is at most $4$