Koszul algebras and regularity

This is a survey paper on commutative Koszul algebras and Castelnuovo-Mumford regularity. We describe several techniques to establish the Koszulness of algebras. We discuss variants of the Koszul property such as strongly Koszul, absolutely Koszul and universally Koszul. We present several open problems related with these notions and their local variants

Fingerprints of the Hierarchical Building up of the Structure on the Mass-Metallicity Relation

We study the mass-metallicity relation of galactic systems with stellar masses larger than 10^9 Mo in Lambda-CDM scenarios by using chemical hydrodynamical simulations. We find that this relation arises naturally as a consequence of the formation of the structure in a hierarchical scenario. The hierarchical building up of the structure determines a characteristic stellar mass at M_c ~10^10.2 Moh^-1 which exhibits approximately solar metallicities from z ~ 3 to z=0. This characteristic mass separates galactic systems in two groups with massive ones forming most of their stars and metals at high redshift. We find evolution in the zero point and slope of the mass-metallicity relation driven mainly by the low mass systems which exhibit the larger variations in the chemical properties. Although stellar mass and circular velocity are directly related, the correlation between circular velocity and metallicity shows a larger evolution with redshift making this relation more appropriate to confront models and observations. The dispersion found in both relations is a function of the stellar mass and reflects the different dynamical history of evolution of the systems.Comment: 4 pages, 4 figures. Accepted MNRAS Letter

Clues for the origin of the fundamental metallicity relations. I: The hierarchical building up of the structure

We analyse the evolutionary history of galaxies formed in a hierarchical scenario consistent with the concordance $\Lambda$-CDM model focusing on the study of the relation between their chemical and dynamical properties. Our simulations consistently describe the formation of the structure and its chemical enrichment within a cosmological context. Our results indicate that the luminosity-metallicity (LZR) and the stellar mass-metallicity (MZR) relations are naturally generated in a hierarchical scenario. Both relations are found to evolve with redshift. In the case of the MZR, the estimated evolution is weaker than that deduced from observational works by approximately 0.10 dex. We also determine a characteristic stellar mass, $M_c \approx 3 \times 10^{10} M_{\odot}$, which segregates the simulated galaxy population into two distinctive groups and which remains unchanged since $z\sim 3$, with a very weak evolution of its metallicity content. The value and role played by $M_c$ is consistent with the characteristic mass estimated from the SDSS galaxy survey by Kauffmann et al. (2004). Our findings suggest that systems with stellar masses smaller than $M_c$ are responsible for the evolution of this relation at least from $z\approx 3$. Larger systems are stellar dominated and have formed more than 50 per cent of their stars at $z \ge 2$, showing very weak evolution since this epoch. We also found bimodal metallicity and age distributions from $z\sim3$, which reflects the existence of two different galaxy populations. Although SN feedback may affect the properties of galaxies and help to shape the MZR, it is unlikely that it will significantly modify $M_c$ since, from $z=3$ this stellar mass is found in systems with circular velocities larger than 100 \kms.Comment: 17 pages, 13 figures. Minor changes to match accepted version. Accepted October 3 MNRA

Milky Way type galaxies in a LCDM cosmology

We analyse a sample of 52,000 Milky Way (MW) type galaxies drawn from the publicly available galaxy catalogue of the Millennium Simulation with the aim of studying statistically the differences and similarities of their properties in comparison to our Galaxy. Model galaxies are chosen to lie in haloes with maximum circular velocities in the range 200-250 km/seg and to have bulge-to-disk ratios similar to that of the Milky Way. We find that model MW galaxies formed quietly through the accretion of cold gas and small satellite systems. Only 12 per cent of our model galaxies experienced a major merger during their lifetime. Most of the stars formed in situ, with only about 15 per cent of the final mass gathered through accretion. Supernovae and AGN feedback play an important role in the evolution of these systems. At high redshifts, when the potential wells of the MW progenitors are shallower, winds driven by supernovae explosions blow out a large fraction of the gas and metals. As the systems grow in mass, SN feedback effects decrease and AGN feedback takes over, playing a more important role in the regulation of the star formation activity at lower redshifts. Although model Milky Way galaxies have been selected to lie in a narrow range of maximum circular velocities, they nevertheless exhibit a significant dispersion in the final stellar masses and metallicities. Our analysis suggests that this dispersion results from the different accretion histories of the parent dark matter haloes. Statically, we also find evidences to support the Milky Way as a typical Sb/Sc galaxy in the same mass range, providing a suitable benchmark to constrain numerical models of galaxy formationComment: 10 pages, 7 figures, mne2.cls, MNRAS, replaced with accepted versio