Moduli Space of Quasi-Maps from P^{1} with Two Marked Points to P(1,1,1,3) and j-invariant

In this paper, we construct toric data of moduli space of quasi maps of degree $d$ from P^{1} with two marked points to weighted projective space P(1.1,1,3). With this result, we prove that the moduli space is a compact toric orbifold. We also determine its Chow ring. Moreover, we give a proof of the conjecture proposed by Jinzenji that a series of intersection numbers of the moduli spaces coincides with expansion coefficients of inverse function of -log(j(tau)).Comment: 22 pages, minor errors are corrected, references are added, some comments are added in Introductio

Evidence for Infalling Gas of Low Angular Momentum towards the L1551 NE Keplerian Circumbinary Disk

We report follow-up observations of the Class I binary protostellar system L1551 NE in the C18O (3--2) line with the SMA in its compact and subcompact configurations. Our previous observations at a higher angular resolution in the extended configuration revealed a circumbinary disk exhibiting Keplerian motion. The combined data having more extensive spatial coverage (~140 - 2000 AU) verify the presence of a Keplerian circumbinary disk, and reveals for the first time a distinct low-velocity (~< +-0.5 km s-1 from the systemic velocity) component that displays a velocity gradient along the minor axis of the circumbinary disk. Our simple model that reproduces the main features seen in the Position-Velocity diagrams comprises a circumbinary disk exhibiting Keplerian motion out to a radius of ~300 AU, beyond which the gas exhibits pure infall at a constant velocity of ~0.6 km s-1. The latter is significantly smaller than the expected free-fall velocity of ~2.2 km s-1 onto the L1551 NE protostellar mass of ~0.8 Msun at ~300 AU, suggesting that the infalling gas is decelerated as it moves into regions of high gas pressure in the circumbinary disk. The discontinuity in angular momenta between the outer infalling gas and inner Keplerian circumbinary disk implies an abrupt transition in the effectiveness at which magnetic braking is able to transfer angular momentum outwards, a result perhaps of the different plasma beta and ionization fractions between the outer and inner regions of the circumbinary disk.Comment: 23 pages, 5 figure

Multiplicity at early stages of star formation, small clusters. Observations Overview

The SOLA (Soul of Lupus with ALMA) project is conducting comprehensive studies of the Lupus Molecular Clouds and their star formation processes covering 10-10^4 AU scale. Our goal is to exploit ALMA and other facilities over a wide wavelength range to establish a prototypical low-mass star forming scenario based on the Lupus region. In the presentation, we will focus on angular momentum in dense cores in a filament, molecular outflows from young stars, and Class 0/I binary survey in Lupus as well as overview of our projects. Our binary survey was conducted in ALMA cycle 2 and achieved at 0.2-0.3 arcsec resolution discovering new binary systems in Lupus. At the same time, we obtained EX Lup, EXor type burst source, data in ALMA Cycle 3