Classification of Moduli Spaces of Arrangements of 9 Projective Lines

In this paper, we present a proof that the list of the classification of arrangements of 9 lines by Nazir and Yoshinaga is complete.Comment: Changed notations in the definition of moduli space to improve clarity. Results unchange

Global Generation of Adjoint Line Bundles on Projective 55-folds

Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$ such that $L^5>7^5$ and $L^d\cdot Z\geq 7^d$ for any subvariety $Z$ of dimension $1\leq d\leq 4$. We show that $\mathcal{O}_X(K_X+L)$ is globally generated.Comment: Final version to appear in manuscripta mathematica. We notice that mistakes were introduced by the journal to some fractions in the form "expression/expression" which should be read as "(expression)/(expression)

Progenitor delay-time distribution of short gamma-ray bursts: Constraints from observations

Context. The progenitors of short gamma-ray bursts (SGRBs) have not yet been well identified. The most popular model is the merger of compact object binaries (NS-NS/NS-BH). However, other progenitor models cannot be ruled out. The delay-time distribution of SGRB progenitors, which is an important property to constrain progenitor models, is still poorly understood. Aims. We aim to better constrain the luminosity function of SGRBs and the delay-time distribution of their progenitors with newly discovered SGRBs. Methods. We present a low-contamination sample of 16 Swift SGRBs that is better defined by a duration shorter than 0.8 s. By using this robust sample and by combining a self-consistent star formation model with various models for the distribution of time delays, the redshift distribution of SGRBs is calculated and then compared to the observational data. Results. We find that the power-law delay distribution model is disfavored and that only the lognormal delay distribution model with the typical delay tau >= 3 Gyr is consistent with the data. Comparing Swift SGRBs with T90 > 0.8 s to our robust sample (T90 < 0.8 s), we find a significant difference in the time delays between these two samples. Conclusions. Our results show that the progenitors of SGRBs are dominated by relatively long-lived systems (tau >= 3 Gyr), which contrasts the results found for Type Ia supernovae. We therefore conclude that primordial NS-NS systems are not favored as the dominant SGRB progenitors. Alternatively, dynamically formed NS-NS/BH and primordial NS-BH systems with average delays longer than 5 Gyr may contribute a significant fraction to the overall SGRB progenitors.Comment: 8 pages, 6 figures, Astron. Astrophys. in pres