Derived factorization categories of non-Thom--Sebastiani-type sums of potentials

We first prove semi-orthogonal decompositions of derived factorization categories arising from sums of potentials of gauged Landau-Ginzburg models, where the sums are not necessarily Thom--Sebastiani type. We then apply the result to the category \HMF^{L_f}(f) of maximally graded matrix factorizations of an invertible polynomial $f$ of chain type, and explicitly construct a full strong exceptional collection E_1,\hdots,E_{\mu} in \HMF^{L_f}(f) whose length $\mu$ is the Milnor number of the Berglund--H\"ubsch transpose $\widetilde{f}$ of $f$. This proves a conjecture, which postulates that for an invertible polynomial $f$ the category \HMF^{L_f}(f) admits a tilting object, in the case when $f$ is a chain polynomial. Moreover, by careful analysis of morphisms between the exceptional objects $E_i$, we explicitly determine the quiver with relations $(Q,I)$ which represents the endomorphism ring of the associated tilting object $\oplus_{i=1}^{\mu}E_i$ in \HMF^{L_f}(f), and in particular we obtain an equivalence \HMF^{L_f}(f)\cong \Db(\fmod kQ/I).Comment: Major improvements. The proof of the existence of a tilting object is added, and we compute the associated quiver with relations. 48 page

Keck Spectroscopy of Faint 3<z<7 Lyman Break Galaxies:- II. A High Fraction of Line Emitters at Redshift Six

As Lyman-alpha photons are scattered by neutral hydrogen, a change with redshift in the Lyman-alpha equivalent width distribution of distant galaxies offers a promising probe of the degree of ionization in the intergalactic medium and hence when cosmic reionization ended. This simple test is complicated by the fact that Lyman-alpha emission can also be affected by the evolving astrophysical details of the host galaxies. In the first paper in this series, we demonstrated both a luminosity and redshift dependent trend in the fraction of Lyman-alpha emitters seen within color-selected Lyman-break galaxies (LBGs) over the range 3<z<6; lower luminosity galaxies and those at higher redshift show an increased likelihood of strong emission. Here we present the results from much deeper 12.5 hour exposures with the Keck DEIMOS spectrograph focused primarily on LBGs at z~6 which enable us to confirm the redshift dependence of line emission more robustly and to higher redshift than was hitherto possible. We find 54+/-11% of faint z~6 LBGs show strong (W_0>25 A) emission, an increase of 1.6x from a similar sample observed at z~4. With a total sample of 74 z~6 LBGs, we determine the luminosity-dependent Lyman-alpha equivalent width distribution. Assuming continuity in these trends to the new population of z~7 sources located with the Hubble WFC3/IR camera, we predict that unless the neutral fraction rises in the intervening 200 Myr, the success rate for spectroscopic confirmation using Lyman-alpha emission should be high.Comment: 6 pages, 3 figures, submitted to ApJ

Radii and Mass-loss Rates of Type IIb Supernova Progenitors

Several Type IIb supernovae (SNe IIb) have been extensively studied, both in terms of the progenitor radius and the mass-loss rate in the final centuries before the explosion. While the sample is still limited, evidence has been accumulating that the final mass-loss rate tends to be larger for a more extended progenitor, with the difference exceeding an order of magnitude between the more and less extended progenitors. The high mass-loss rates inferred for the more extended progenitors are not readily explained by a prescription commonly used for a single stellar wind. In this paper, we calculate a grid of binary evolution models. We show that the observational relation in the progenitor radii and mass-loss rates may be a consequence of non-conservative mass transfer in the final phase of progenitor evolution without fine tuning. Further, we find a possible link between SNe IIb and SNe IIn. The binary scenario for SNe IIb inevitably leads to a population of SN progenitors surrounded by dense circumstellar matter (CSM) due to extensive mass loss ($\dot{M} \gtrsim 10^{-4} M_{\odot} \mathrm{yr}^{-1}$) in the binary origin. About 4% of all observed SNe IIn are predicted to have dense CSM, produced by binary non-conservative mass transfer, whose observed characteristics are distinguishable from SNe IIn from other scenarios. Indeed, such SNe may be observationally dominated by systems experiencing huge mass loss in the final $10^3$ yr, leading to luminous SNe IIn or initially bright SNe IIP or IIL with characteristics of SNe IIn in their early spectra.Comment: 18 pages, 12 figures, Accepted for publication in The Astrophysical Journa