Discriminant loci of ample and spanned line bundles

Let $(X,L,V)$ be a triplet where $X$ is an irreducible smooth complex projective variety, $L$ is an ample and spanned line bundle on $X$ and $V\subseteq H^0(X,L)$ spans $L$. The discriminant locus \Cal D(X,V) \subset |V| is the algebraic subset of singular elements of $|V|$. We study the components of \Cal D(X,V) in connection with the jumping sets of $(X,V)$, generalizing the classical biduality theorem. We also deal with the degree of the discriminant (codegree of $(X,L,V)$) giving some bounds on it and classifying curves and surfaces of codegree 2 and 3. We exclude the possibility for the codegree to be 1. Significant examples are provided

Global Games with Strategic Substitutes

In this paper we use a non cooperative equilibrium selection approach as a notion of stability in link formation games. Specifically, we follow the global games approach first introduced by Carlsson and van Damme (1993), to study the robustness of the set of Nash equilibria for a class of link formation games in strategic form with supermodular payo. functions. Interestingly, the equilibrium selected is in conflict with those predicted by the traditional cooperative refinements. Moreover, we get a conflict between stability and e.ciency even when no such conflict exists with the cooperative refinements. We discuss some practical issues that these di.erent theoretical approaches raise in reality. The paper also provides an extension of the global game theory that can be applied beyond network literature.Games, Networks, Equilibrium Selection.

Stability and Equilibrium Selection in a Link Formation Game

In this paper we use a non cooperative equilibrium selection approach as a notion of stability in link formation games. Specifically, we follow the global games approach first introduced by Carlsson and van Damme (1993), to study the robustness of the set of Nash equilibria for a class of link formation games in strategic form with supermodular payoff functions. Interestingly, the equilibrium selected is in conflict with those predicted by the traditional cooperative refinements. Moreover, we get a conflict between stability and efficiency even when no such conflict exists with the cooperative refinements. We discuss some practical issues that these different theoretical approaches raise in reality. The paper also provides an extension of the global game theory that can be applied beyond network literature.Global Games, Equilibrium Selection, Networks.

Tangential projections and secant defective varieties

Going one step further in Zak's classification of Scorza varieties with secant defect equal to one, we characterize the Veronese embedding of $\P^n$ given by the complete linear system of quadrics and its smooth projections from a point as the only smooth irreducible complex and non-degenerate projective subvarieties of $\P^N$ that can be projected isomorphically into $\P^{2n}$ when $N\geq\binom{n+2}{2}-2$.Comment: To appear in Bulletin of the London Mathematical Societ

HIV-1 Gag trafficking and assembly: mathematical models and numerical simulations

2013 Fall.Includes bibliographical references.AIDS (acquired immune deficiency syndrome) is an infectious disease that takes away many people's lives each year. Group-specific antigen (Gag) polyprotein precursor is the major structural component of HIV, the causing agent of AIDS. Gag is essential and sufficient for the formation of new HIV virus-like particles. The late stages of the HIV-1 life cycle include the transport of Gag proteins towards the cell membrane, the oligomerization of Gag near the cell membrane during the budding process, and core assembly during virion maturation. The mechanisms for Gag protein trafficking and assembly are not yet fully understood. In order to gain further insight into the mechanisms of HIV-1 replication, we develop and analyze mathematical models and numerical algorithms for intracellular Gag protein trafficking, Gag trimerization near the cell membrane, and HIV-1 core assembly. Our preliminary results indicate that active transport plays an important role for Gag trafficking in the cytoplasm. This process can be mathematically modeled by convection-diffusion equations, which can be solved efficiently using characteristic finite element methods. We employ differential dynamical systems to model Gag trimerization and HIV-1 core assembly. For the Gag trimerization model, we estimate relationships between the association and dissociation parameters as well as the Gag arrival and multimerization parameters. We also find expressions for the equilibrium concentrations of the monomer and trimer species, and show that the equilibrium is asymptotically stable. For HIV-1 core assembly, we first consider a model developed by Zlonick and others, which regards assembly as a polymerization reaction. We utilize theoretical and numerical tools to confirm the stability of the equilibrium of CA intermediates. In addition, we propose a cascaded dynamical system model for HIV-1 core assembly. The model consists of two subsystems: one subsystem for nucleation and one for elongation. We perform simulations on the nucleation model, which suggests the existence of an equilibrium of the CA species

The circumstellar medium of the peculiar supernova SN1997ab

We report the detection of the slow moving wind into which the compact supernova remnant SN 1997ab is expanding. Echelle spectroscopy provides clear evidence for a well resolved narrow (Full Width at Zero Intensity, FWZI ~ 180 km/s) P-Cygni profile, both in Ha and Hb, superimposed on the broad emission lines of this compact supernova remnant. From theoretical arguments we know that the broad and strong emission lines imply a circumstellar density (n ~ 10^7 cm^-3). This, together with our detection, implies a massive and slow stellar wind experienced by the progenitor star shortly prior to the explosion.Comment: 10 pages, 2 figures, acepted for publication in MNRAS. Uses referee.sty, psfig.sty and mn.sty. A postscript file can also be retrieved at http://www.strw.LeidenUniv.nl/~salamanc/latest.htm