Relative Čech–Dolbeault homology and applications

We define the relative Dolbeault homology of a complex manifold with currents via a Čech approach, and we prove its equivalence with the relative Čech–Dolbeault cohomology as defined by Suwa (in: Singularities–Niigata–Toyama 2007. Advanced studies in pure mathematics, vol 56. Mathematical Society of Japan, Tokyo, pp 321–340, 2009). This definition is then used to compare the relative Dolbeault cohomology groups of two complex manifolds of the same dimension related by a suitable proper surjective holomorphic map. Finally, an application to blow-ups is considered and a blow-up formula for the Dolbeault cohomology in terms of relative cohomology is presented

Some remarks on Hermitian manifolds satisfying Kähler-like conditions

We study Hermitian metrics whose Bismut connection ∇ B satisfies the first Bianchi identity in relation to the SKT condition and the parallelism of the torsion of the Bimut connection. We obtain a characterization of complex surfaces admitting Hermitian metrics whose Bismut connection satisfy the first Bianchi identity and the condition RB(x, y, z, w) = RB(Jx, Jy, z, w) , for every tangent vectors x, y, z, w, in terms of Vaisman metrics. These conditions, also called Bismut Kähler-like, have been recently studied in Angella et al. (Commun Anal Geom, to appear, 2018), Yau et al. (2019) and Zhao and Zheng (2019). Using the characterization of SKT almost abelian Lie groups in Arroyo and Lafuente (Proc Lond Math Soc (3) 119:266–289, 2019), we construct new examples of Hermitian manifolds satisfying the Bismut Kähler-like condition. Moreover, we prove some results in relation to the pluriclosed flow on complex surfaces and on almost abelian Lie groups. In particular, we show that, if the initial metric has constant scalar curvature, then the pluriclosed flow preserves the Vaisman condition on complex surfaces

Variational Problems in Conformal Geometry

We study the Euler–Lagrange equation for several natural functionals defined on a conformal class of almost Hermitian metrics, whose expression involves the Lee form θ of the metric. We show that the Gauduchon metrics are the unique extremal metrics of the functional corresponding to the norm of the codifferential of the Lee form. We prove that on compact complex surfaces, in every conformal class there exists a unique metric, up to multiplication by a constant, which is extremal for the functional given by the L2-norm of d Jθ, where J denotes the complex structure. These extremal metrics are not the Gauduchon metrics in general, hence we extend their definition to any dimension and show that they give unique representatives, up to constant multiples, of any conformal class of almost Hermitian metrics

Complex symplectic lie algebras with large abelian subalgebras

We present two constructions of complex symplectic structures on Lie algebras with large Abelian ideals. In particular, we completely classify complex symplectic structures on almost Abelian Lie algebras. By considering compact quotients of their corresponding connected, simply connected Lie groups we obtain many examples of complex symplectic manifolds which do not carry (hyper)kähler metrics. We also produce examples of compact complex symplectic manifolds endowed with a fibration whose fibers are Lagrangian tori

Transport and turbulence studies in the linear ohmic confinement regime in Alcator C-Mod

Transport in ohmically heated plasmas in Alcator C-Mod was studied in both the linear (LOC) and saturated (SOC) ohmic L-mode confinement regimes and the importance of turbulent transport in the region r/a = 0.5–0.8 was established. After an extensive analysis with TGLF and GYRO, it is found that using an effective impurity ion species with Z[subscript i] = 8, and moderately high Z[subscript eff] (2.0–5.6), in the LOC regime electron transport becomes dominant due to TEM turbulence. The key ingredient in the present results is the observation that dilution of the main ion species (deuterium) by impurity species of moderate charge state reduces dominant ITG turbulence, in contrast to the SOC regime with little, if any dilution. The turbulent spectrum measured with the phase contrast imaging (PCI) diagnostic is in qualitative agreement with predictions of a synthetic PCI diagnostic adopted to Global GYRO. The toroidal rotation in the low-density LOC regime is in the co-current direction but as the density is raised in the SOC regime the rotation reverses to the counter current drive direction. The impurity content of the plasma was measured recently and an effective Z[subscript i] of 9 was deduced.United States. Dept. of Energy (Grant DE-FC02-99ER54512-CMOD

Gyrokinetic study of turbulence suppression in a JET-ILW power scan

For exploring tokamak operation regimes that deliver both high beta and good energy confinement, power scans at JET with ITER-like wall have been performed. Relatively weak degradation of the confinement time coincides with increased core temperature of the ions at high power. The changes in core turbulence characteristics during a power scan with an optimized (broad) q profile are analyzed by means of nonlinear gyrokinetic simulations. The increase in beta is crucial for stabilizing ion temperature gradient driven turbulence, accompanied by increased ion to electron temperature ratio, the presence of a dynamic fast ion species, as well as the geometric stabilization by increased thermal and suprathermal pressure. A sensitivity study with respect to the q profile reveals that electromagnetic effects are more pronounced at larger values of q. Further, it is confirmed that turbulence suppression due to rotation becomes less effective in such strongly electromagnetic systems. Electrostatic simplified models may thus perform well in present-day devices, in which high beta is often correlated with high rotation, but provide poor extrapolation towards low rotation devices. Implications for ITER and reactor plasmas are discussed.</p