Monomial transformations of the projective space

We prove that, over any field, the dimension of the indeterminacy locus of a rational transformation $f$ of $P^n$ which is defined by monomials of the same degree $d$ with no common factors is at least $(n-2)/2$, provided that the degree of $f$ as a map is not divisible by $d$. This implies upper bounds on the multidegree of $f$

Ground-Based Multisite Observations of Two Transits of HD 80606b

We present ground-based optical observations of the 2009 September and 2010 January transits of HD 80606b. Based on three partial light curves of the 2009 September event, we derive a midtransit time of T_c [HJD] = 2455099.196 ± 0.026, which is about 1σ away from the previously predicted time. We observed the 2010 January event from nine different locations, with most phases of the transit being observed by at least three different teams. We determine a midtransit time of Tc [HJD] = 2455210.6502 ± 0.0064, which is within 1.3σ of the time derived from a Spitzer observation of the same event

Stringy K-theory and the Chern character

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new ring called the full orbifold K-theory of Y. For a global quotient Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra of the full orbifold K-theory of the the stack Y and is linearly isomorphic to the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a different, ``quantum,'' product, which respects the natural group grading. We prove there is a ring isomorphism, the stringy Chern character, from stringy K-theory to stringy cohomology, and a ring homomorphism from full orbifold K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy Grothendieck-Riemann-Roch for etale maps. We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's construction. Since our constructions do not use complex curves, stable maps, admissible covers, or moduli spaces, our results simplify the definitions of Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of Abramovich-Graber-Vistoli's orbifold Chow. We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler Resolution Conjecture holds for symmetric products. Our results hold both in the algebro-geometric category and in the topological category for equivariant almost complex manifolds.Comment: Exposition improved and additional details provided. To appear in Inventiones Mathematica

Classification of double flag varieties of complexity 0 and 1

A classification of double flag varieties of complexity 0 and 1 is obtained. An application of this problem to decomposing tensor products of irreducible representations of semisimple Lie groups is considered

Heisenberg antiferromagnet on the square lattice for S>=1

Theoretical predictions of a semiclassical method - the pure-quantum self-consistent harmonic approximation - for the correlation length and staggered susceptibility of the Heisenberg antiferromagnet on the square lattice (2DQHAF) agree very well with recent quantum Monte Carlo data for S=1, as well as with experimental data for the S=5/2 compounds Rb2MnF4 and KFeF4. The theory is parameter-free and can be used to estimate the exchange coupling: for KFeF4 we find J=2.33 +- 0.33 meV, matching with previous determinations. On this basis, the adequacy of the quantum nonlinear sigma model approach in describing the 2DQHAF when S>=1 is discussed.Comment: 4 pages RevTeX file with 5 figures included by psfi

HATS-8b: A Low-Density Transiting Super-Neptune

HATS-8b is a low density transiting super-Neptune discovered as part of the HATSouth project. The planet orbits its solar-like G-dwarf host (V = 14.03 ± 0.10, T_(eff) = 5679 ± 50 K) with a period of 3.5839 days. HATS-8b is the third lowest-mass transiting exoplanet to be discovered from a wide-field ground-based search, and with a mass of 0.138 ± 0.019 M_J it is approximately halfway between the masses of Neptune and Saturn. However, HATS-8b has a radius of 0.873_(-0.075)^(+0.123) R_J, resulting in a bulk density of just 0.259 ± 0.091 g cm^(-3). The metallicity of the host star is super-solar ([Fe/H] = 0.210 ± 0.080), providing evidence against the idea that low-density exoplanets form from metal-poor environments. The low density and large radius of HATS-8b results in an atmospheric scale height of almost 1000 km, and in addition to this there is an excellent reference star of nearly equal magnitude at just 19" separation in the sky. These factors make HATS-8b an exciting target for future atmospheric characterization studies, particularly for long-slit transmission spectroscopy

HATS-15b and HATS-16b: Two Massive Planets Transiting Old G Dwarf Stars

We report the discovery of HATS-15 b and HATS-16 b, two massive transiting extrasolar planets orbiting evolved (~10 Gyr) main-sequence stars. The planet HATS-15 b, which is hosted by a G9 V star (V = 14.8 mag), is a hot Jupiter with mass of 2.17 ± 0.15 M_J and radius of 1.105 ± 0.040 R_J, and it completes its orbit in about 1.7 days. HATS-16 b is a very massive hot Jupiter with mass of 3.27 ± 0.19 M_J and radius of 1.30 ± 0.15 R_J; it orbits around its G3 V parent star (V = 13.8 mag) in ~2.7 days. HATS-16 is slightly active and shows a periodic photometric modulation, implying a rotational period of 12 days, which is unexpectedly short given its isochronal age. This fast rotation might be the result of the tidal interaction between the star and its planet

HATS-7b: A Hot Super Neptune Transiting a Quiet K Dwarf Star

We report the discovery by the HATSouth network of HATS-7b, a transiting Super-Neptune with a mass of 0.120 ± 0.012 M_J, a radius of 0.563_(-0.034)^(+0.046) R_J, and an orbital period of 3.1853 days. The host star is a moderately bright (V = 13.340 ± 0.010 mag, K_S = 10.976 ± 0.026 mag) K dwarf star with a mass of 0.849 ± 0.027 M_⊙, a radius of 0.815_(-0.035)^(+0.049) R_⊙, and a metallicity of [Fe/H] = + 0.250 ± 0.080. The star is photometrically quiet to within the precision of the HATSouth measurements, has low RV jitter, and shows no evidence for chromospheric activity in its spectrum. HATS-7b is the second smallest radius planet discovered by a wide-field ground-based transit survey, and one of only a handful of Neptune-size planets with mass and radius determined to 10% precision. Theoretical modeling of HATS-7b yields a hydrogen–helium fraction of 18 ± 4% (rock-iron core and H_2–He envelope), or 9 ± 4% (ice core and H_2–He envelope), i.e., it has a composition broadly similar to that of Uranus and Neptune, and very different from that of Saturn, which has 75% of its mass in H_2–He. Based on a sample of transiting exoplanets with accurately (<20%) determined parameters, we establish approximate power-law relations for the envelopes of the mass–density distribution of exoplanets. HATS-7b, which, together with the recently discovered HATS-8b, is one of the first two transiting super-Neptunes discovered in the Southern sky, is a prime target for additional follow-up observations with Southern hemisphere facilities to characterize the atmospheres of Super-Neptunes (which we define as objects with mass greater than that of Neptune, and smaller than halfway between that of Neptune and Saturn, i.e., 0.054 M_J < M_p < 0.18 M_J)