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Chen Jiang

Publications and source records attributed to Chen Jiang.

125 records · Page 7Linked to original sources
arXiv2019

On the anti-canonical geometry of weak $\mathbb{Q}$-Fano threefolds, II

By a canonical (resp. terminal) weak $\mathbb{Q}$-Fano $3$-fold we mean a normal projective one with at worst canonical (resp. terminal) singularities on which the anti-canonical divisor is $\mathbb{Q}$-Cartier, nef and big. For a canonical weak $\mathbb{Q}$-Fano $3$-fold $V$, we show that there exists a terminal weak $\mathbb{Q}$-Fano $3$-fold $X$, being birational to $V$, such that the $m$-th anti-canonical map defined by $|-mK_{X}|$ is birational for all $m\geq 52$. As an intermediate result, we show that for any $K$-Mori fiber space $Y$ of a canonical weak $\mathbb{Q}$-Fano $3$-fold, the $m$-th anti-canonical map defined by $|-mK_{Y}|$ is birational for all $m\geq 52$.

math.AG↗
arXiv2019

Remarks on Kawamata's effective non-vanishing conjecture for manifolds with trivial first Chern classes

Kawamata proposed a conjecture predicting that every nef and big line bundle on a smooth projective variety with trivial first Chern class has nontrivial global sections. We verify this conjecture for several cases, including (i) all hyperkähler varieties of dimension $\leq 6$; (ii) all known hyperkähler varieties except for O'Grady's 10-dimensional example; (iii) general complete intersection Calabi-Yau varieties in certain Fano manifolds (e.g. toric ones). Moreover, we investigate the effectivity of Todd classes of hyperkähler varieties and Calabi-Yau varieties. We prove that the fourth Todd classes are "fakely effective" for all hyperkähler varieties and general complete intersection Calabi-Yau varieties in products of projective spaces.

math.AG↗
arXiv2019

The Noether inequality for algebraic threefolds (With an Appendix by János Kollár)

We establish the Noether inequality for projective $3$-folds. More precisely, we prove that the inequality $${\rm vol}(X)\geq \tfrac{4}{3}p_g(X)-{\tfrac{10}{3}}$$ holds for all projective $3$-folds $X$ of general type with either $p_g(X)\leq 4$ or $p_g(X)\geq 21$, where $p_g(X)$ is the geometric genus and ${\rm vol}(X)$ is the canonical volume. This inequality is optimal due to known examples found by M. Kobayashi in 1992.

math.AG↗
arXiv2019

A Hot Saturn Orbiting An Oscillating Late Subgiant Discovered by TESS

We present the discovery of TOI-197.01, the first transiting planet identified by the Transiting Exoplanet Survey Satellite (TESS) for which asteroseismology of the host star is possible. TOI-197 (HIP116158) is a bright (V=8.2 mag), spectroscopically classified subgiant which oscillates with an average frequency of about 430 muHz and displays a clear signature of mixed modes. The oscillation amplitude confirms that the redder TESS bandpass compared to Kepler has a small effect on the oscillations, supporting the expected yield of thousands of solar-like oscillators with TESS 2-minute cadence observations. Asteroseismic modeling yields a robust determination of the host star radius (2.943+/-0.064 Rsun), mass (1.212 +/- 0.074 Msun) and age (4.9+/-1.1 Gyr), and demonstrates that it has just started ascending the red-giant branch. Combining asteroseismology with transit modeling and radial-velocity observations, we show that the planet is a "hot Saturn" (9.17+/-0.33 Rearth) with an orbital period of ~14.3 days, irradiance of 343+/-24 Fearth, moderate mass (60.5 +/- 5.7 Mearth) and density (0.431+/-0.062 gcc). The properties of TOI-197.01 show that the host-star metallicity - planet mass correlation found in sub-Saturns (4-8 Rearth) does not extend to larger radii, indicating that planets in the transition between sub-Saturns and Jupiters follow a relatively narrow range of densities. With a density measured to ~15%, TOI-197.01 is one of the best characterized Saturn-sized planets to date, augmenting the small number of known transiting planets around evolved stars and demonstrating the power of TESS to characterize exoplanets and their host stars using asteroseismology.

astro-ph.EP↗
arXiv2019

Video Object Segmentation using Teacher-Student Adaptation in a Human Robot Interaction (HRI) Setting

Video object segmentation is an essential task in robot manipulation to facilitate grasping and learning affordances. Incremental learning is important for robotics in unstructured environments, since the total number of objects and their variations can be intractable. Inspired by the children learning process, human robot interaction (HRI) can be utilized to teach robots about the world guided by humans similar to how children learn from a parent or a teacher. A human teacher can show potential objects of interest to the robot, which is able to self adapt to the teaching signal without providing manual segmentation labels. We propose a novel teacher-student learning paradigm to teach robots about their surrounding environment. A two-stream motion and appearance "teacher" network provides pseudo-labels to adapt an appearance "student" network. The student network is able to segment the newly learned objects in other scenes, whether they are static or in motion. We also introduce a carefully designed dataset that serves the proposed HRI setup, denoted as (I)nteractive (V)ideo (O)bject (S)egmentation. Our IVOS dataset contains teaching videos of different objects, and manipulation tasks. Unlike previous datasets, IVOS provides manipulation tasks sequences with segmentation annotation along with the waypoints for the robot trajectories. It also provides segmentation annotation for the different transformations such as translation, scale, planar rotation, and out-of-plane rotation. Our proposed adaptation method outperforms the state-of-the-art on DAVIS and FBMS with 6.8% and 1.2% in F-measure respectively. It improves over the baseline on IVOS dataset with 46.1% and 25.9% in mIoU.

cs.CV↗
arXiv2017

Torsion exceptional sheaves on weak del Pezzo surfaces of Type A

We investigate torsion exceptional sheaves on a weak del Pezzo surface of degree greater than two whose anticanonical model has at most $A_n$-singularities. We show that every torsion exceptional sheaf can be obtained from a line bundle on a $(-1)$-curve by acting spherical twist functors successively.

math.AG↗
arXiv2017

On birational boundedness of Fano fibrations

We investigate birational boundedness of Fano varieties and Fano fibrations. We establish an inductive step towards birational boundedness of Fano fibrations via conjectures related to boundedness of Fano varieties and Fano fibrations. As corollaries, we provide approaches towards birational boundedness and boundedness of anti-canonical volumes of varieties of $ε$-Fano type. Furthermore, we show birational boundedness of $3$-folds of $ε$-Fano type.

math.AG↗
arXiv2016

On Fujita invariants of subvarieties of a uniruled variety

We show that if $X$ is a smooth uniruled projective variety and $L$ a big and semiample $\mathbb{Q}$-divisor on $X$, then there exists a proper closed subset $W\subset X$ such that every subvariety $Y$ satisfying $a(Y,L)> a(X,L)$ is contained in $W$.

math.AG↗
arXiv2016

On irregular threefolds and fourfolds with numerically trivial canonical bundle

We prove that for a smooth projective irregular $3$-fold $X$ with $K_X\equiv 0$ and a nef and big divisor $L$ on $X$, $|mL+P|$ gives a birational map for all $m\geq 3$ and all $P\in \text{Pic}^0(X)$. We also use the same method to deal with $4$-folds, and prove that for a smooth projective irregular $4$-fold $X$ with $K_X\equiv 0$ and an ample divisor $L$ on $X$, $|mL+P|$ gives a birational map for all $m\geq 5$ and all $P\in \text{Pic}^0(X)$. These results are also optimal.

math.AG↗
arXiv2015

Kepler-432: a red giant interacting with one of its two long period giant planets

We report the discovery of Kepler-432b, a giant planet ($M_b = 5.41^{+0.32}_{-0.18} M_{\rm Jup}, R_b = 1.145^{+0.036}_{-0.039} R_{\rm Jup}$) transiting an evolved star $(M_\star = 1.32^{+0.10}_{-0.07} M_\odot, R_\star = 4.06^{+0.12}_{-0.08} R_\odot)$ with an orbital period of $P_b = 52.501129^{+0.000067}_{-0.000053}$ days. Radial velocities (RVs) reveal that Kepler-432b orbits its parent star with an eccentricity of $e = 0.5134^{+0.0098}_{-0.0089}$, which we also measure independently with asterodensity profiling (AP; $e=0.507^{+0.039}_{-0.114}$), thereby confirming the validity of AP on this particular evolved star. The well-determined planetary properties and unusually large mass also make this planet an important benchmark for theoretical models of super-Jupiter formation. Long-term RV monitoring detected the presence of a non-transiting outer planet (Kepler-432c; $M_c \sin{i_c} = 2.43^{+0.22}_{-0.24} M_{\rm Jup}, P_c = 406.2^{+3.9}_{-2.5}$ days), and adaptive optics imaging revealed a nearby (0\farcs87), faint companion (Kepler-432B) that is a physically bound M dwarf. The host star exhibits high signal-to-noise asteroseismic oscillations, which enable precise measurements of the stellar mass, radius and age. Analysis of the rotational splitting of the oscillation modes additionally reveals the stellar spin axis to be nearly edge-on, which suggests that the stellar spin is likely well-aligned with the orbit of the transiting planet. Despite its long period, the obliquity of the 52.5-day orbit may have been shaped by star-planet interaction in a manner similar to hot Jupiter systems, and we present observational and theoretical evidence to support this scenario. Finally, as a short-period outlier among giant planets orbiting giant stars, study of Kepler-432b may help explain the distribution of massive planets orbiting giant stars interior to 1 AU.

astro-ph.EP↗
arXiv2015

On the anti-canonical geometry of $\mathbb{Q}$-Fano 3-folds

For a $\mathbb{Q}$-Fano 3-fold $X$ on which $K_X$ is a canonical divisor, we investigate the geometry induced from the linear system $|-mK_X|$ in this paper and prove that the anti-$m$-canonical map $φ_{-m}$ is birational onto its image for all $m\geq 39$. By a weak $\mathbb{Q}$-Fano 3-fold $X$ we mean a projective one with at worst terminal singularities on which $-K_X$ is $\mathbb{Q}$-Cartier, nef and big. For weak $\mathbb{Q}$-Fano 3-folds, we prove that $φ_{-m}$ is birational onto its image for all $m\geq 97$.

math.AG↗
arXiv2013

Bounding the volumes of singular weak log del Pezzo surfaces

We give an optimal upper bound for the anti-canonical volume of an $ε$-lc weak log del Pezzo surface. Moreover, we consider the relation between the bound of the volume and the Picard number of the minimal resolution of the surface. Furthermore we consider blowing up several points on a Hirzebruch surface in general position and give some examples of smooth weak log del Pezzo surfaces.

math.AG↗
arXiv2011

Modeling Kepler Observations of Solar-like Oscillations in the Red-giant Star HD 186355

We have analysed oscillations of the red giant star HD 186355 observed by the NASA Kepler satellite. The data consist of the first five quarters of science operations of Kepler, which cover about 13 months. The high-precision time-series data allow us to accurately extract the oscillation frequencies from the power spectrum. We find the frequency of the maximum oscillation power, ν_max, and the mean large frequency separation, Δν, are around 106 and 9.4 μHz respectively. A regular pattern of radial and non-radial oscillation modes is identified by stacking the power spectra in an echelle diagram. We use the scaling relations of Δν and ν_max to estimate the preliminary asteroseismic mass, which is confirmed with the modelling result (M = 1.45 \pm 0.05 M_sun) using the Yale Rotating stellar Evolution Code (YREC7). In addition, we constrain the effective temperature, luminosity and radius from comparisons between observational constraints and models. A number of mixed l = 1 modes are also detected and taken into account in our model comparisons. We find a mean observational period spacing for these mixed modes of about 58 s, suggesting that this red giant branch star is in the shell hydrogen-burning phase.

astro-ph.SR↗