More Like this

1. The CHARA Array Interferometric Program on the Multiplicity of Classical Be Stars: New Detections and Orbits of Stripped Subdwarf Companions

   https://doi.org/10.3847/1538-4357/ad13ec  

   Klement, Robert; Rivinius, Thomas; Gies, Douglas R.; Baade, Dietrich; Mérand, Antoine; Monnier, John D.; Schaefer, Gail H.; Lanthermann, Cyprien; Anugu, Narsireddy; Kraus, Stefan; et al (February 2024, The Astrophysical Journal)

   Abstract Rapid rotation and nonradial pulsations enable Be stars to build decretion disks, where the characteristic line emission forms. A major but unconstrained fraction of Be stars owe their rapid rotation to mass and angular momentum transfer in a binary. The faint, stripped companions can be helium-burning subdwarf OB-type stars (sdOBs), white dwarfs (WDs), or neutron stars. We present optical/near-infrared Center for High Angular Resolution Astronomy (CHARA) interferometry of 37 Be stars selected for spectroscopic indications of low-mass companions. From multiepochH- and/orK-band interferometry plus radial velocities and parallaxes collected elsewhere, we constructed 3D orbits and derived flux ratios and absolute dynamical masses of both components for six objects, quadrupling the number of anchor points for evolutionary models. In addition, a new wider companion was identified for the known Be + sdO binary 59 Cyg, while auxiliary Very Large Telescope Interferometer/GRAVITY spectrointerferometry confirmed circumstellar matter around the sdO companion to HR 2142. On the other hand, we failed to detect any companion to the six Be stars withγCas–like X-ray emission, with sdOB and main-sequence companions of the expected spectroscopic mass being ruled out for the X-ray-prototypical starsγCas andπAqr, leaving elusive WDs as the most likely companions, as well as a likely explanation of the X-rays. No low-mass main-sequence close companions were identified for the other stars. 

   more » « less
2. THE INTEGRAL COHOMOLOGY OF THE HILBERT SCHEME OF TWO POINTS

   https://doi.org/10.1017/fms.2016.5  

   TOTARO, BURT (January 2016, Forum of Mathematics, Sigma)

   null (Ed.)

   The Hilbert scheme $$X^{[a]}$$ of points on a complex manifold $$X$$ is a compactification of the configuration space of $$a$$ -element subsets of $$X$$ . The integral cohomology of $$X^{[a]}$$ is more subtle than the rational cohomology. In this paper, we compute the mod 2 cohomology of $$X^{[2]}$$ for any complex manifold $$X$$ , and the integral cohomology of $$X^{[2]}$$ when $$X$$ has torsion-free cohomology. 

   more » « less
3. Stabilization of the cohomology of thickenings

   Bhatt, Bhargav; Blickle, Manuel; Lyubeznik, Gennady; Singh, Anurag; Zhang, Wenliang. (April 2019, American journal of mathematics)

   For a local complete intersection subvariety $X = V (I)$ in $P^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $$X$$, the cohomology of vector bundles on the formal completion of $P^n$ along $$X$$ can be effectively computed as the cohomology on any sufficiently high thickening $$X_t = V (I^t)$$; the main ingredient here is a positivity result for the normal bundle of $$X$$. Furthermore, we show that the Kodaira vanishing theorem holds for all thickenings $$X_t$$ in the same range of cohomological degrees; this extends the known version of Kodaira vanishing on $$X$$, and the main new ingredient is a version of the Kodaira- Akizuki-Nakano vanishing theorem for $$X$$, formulated in terms of the cotangent complex. 

   more » « less
4. Essential dimension via prismatic cohomology

   https://doi.org/10.1215/00127094-2023-0071  

   Farb, Benson; Kisin, Mark; Wolfson, Jesse (October 2024, Duke Mathematical Journal)

   NA (Ed.)

   For X a smooth, proper complex variety we show that for p≫0, the restriction of the mod p cohomology Hi(X,Fp) to any Zariski open has dimension at least h0,iX . The proof uses the prismatic cohomology of Bhatt and Scholze. We use this result to obtain lower bounds on the p-essential dimension of covers of complex varieties. For example, we prove the p-incompressibility of the mod p homology cover of an abelian variety, confirming a conjecture of Brosnan for sufficiently large p. By combining these techniques with the theory of toroidal compactifications of Shimura varieties, we show that for any Hermitian symmetric domain X, there exist p-congruence covers that are p-incompressible. 

   more » « less
5. Cohomology of finite tensor categories: Duality and Drinfeld centers

   https://doi.org/10.1090/tran/8548  

   Negron, Cris; Plavnik, Julia (March 2022, Transactions of the American Mathematical Society)

   We consider the finite generation property for cohomology of a finite tensor category C \mathscr {C} , which requires that the self-extension algebra of the unit \operatorname {Ext}^\text {\tiny ∙ }_\mathscr {C}(\mathbf {1},\mathbf {1}) is a finitely generated algebra and that, for each object V V in C \mathscr {C} , the graded extension group \operatorname {Ext}^\text {\tiny ∙ }_\mathscr {C}(\mathbf {1},V) is a finitely generated module over the aforementioned algebra. We prove that this cohomological finiteness property is preserved under duality (with respect to exact module categories) and taking the Drinfeld center, under suitable restrictions on C \mathscr {C} . For example, the stated result holds when C \mathscr {C} is a braided tensor category of odd Frobenius-Perron dimension. By applying our general results, we obtain a number of new examples of finite tensor categories with finitely generated cohomology. In characteristic 0 0 , we show that dynamical quantum groups at roots of unity have finitely generated cohomology. We also provide a new class of examples in finite characteristic which are constructed via infinitesimal group schemes. 

   more » « less