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1. Blown-up toric surfaces with non-polyhedral effective cone

   https://doi.org/10.1515/crelle-2023-0022  

   Castravet, Ana-Maria; Laface, Antonio; Tevelev, Jenia; Ugaglia, Luca (May 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We construct projective toric surfaces whose blow-up at a general point has a non-polyhedral pseudo-effective cone.As a consequence, we prove that the pseudo-effective cone of the Grothendieck–Knudsen moduli space ${\overline{M}}_{0,n}$\overline{M}_{0,n}of stable rational curves is not polyhedral for $n\ge 10$n\geq 10.These results hold both in characteristic 0 and in characteristic 𝑝, for all primes 𝑝.Many of these toric surfaces are related to an interesting class of arithmetic threefolds that we call arithmetic elliptic pairs of infinite order.Our analysis relies on tools of arithmetic geometry and Galois representations in the spirit of the Lang–Trotter conjecture, producing toric surfaces whose blow-up at a general point has a non-polyhedral pseudo-effective cone in characteristic 0 and in characteristic 𝑝, for an infinite set of primes 𝑝 of positive density. 

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2. More accurate $$ \sigma \left(\mathcal{GG}\to h\right),\Gamma \left(h\to \mathcal{GG},\mathcal{AA},\overline{\Psi}\Psi \right) $$ and Higgs width results via the geoSMEFT

   https://doi.org/10.1007/JHEP01(2024)170  

   Martin, Adam; Trott, Michael (January 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We develop Standard Model Effective Field Theory (SMEFT) predictions ofσ($$ \mathcal{GG} $$ $\mathrm{GG}$→h), Γ(h→$$ \mathcal{GG} $$ $\mathrm{GG}$), Γ(h→$$ \mathcal{AA} $$ $\mathrm{AA}$) to incorporate full two loop Standard Model results at the amplitude level, in conjunction with dimension eight SMEFT corrections. We simultaneously report consistent Γ(h→$$ \overline{\Psi}\Psi $$ $\overline{\Psi }\Psi$) results including leading QCD corrections and dimension eight SMEFT corrections. This extends the predictions of the former processes Γ, σto a full set of corrections at$$ \mathcal{O}\left({\overline{v}}_T^2/{\varLambda}^2{\left(16{\pi}^2\right)}^2\right) $$ $O\left({\overline{v}}_T^2/{\Lambda }^2{\left(16{\pi }^2\right)}^2\right)$and$$ \mathcal{O}\left({\overline{v}}_T^4/{\Lambda}^4\right) $$ $O\left({\overline{v}}_T^4/{\Lambda }^4\right)$, where$$ {\overline{v}}_T $$ ${\overline{v}}_T$is the electroweak scale vacuum expectation value and Λ is the cut off scale of the SMEFT. Throughout, cross consistency between the operator and loop expansions is maintained by the use of the geometric SMEFT formalism. For Γ(h→$$ \overline{\Psi}\Psi $$ $\overline{\Psi }\Psi$), we include results at$$ \mathcal{O}\left({\overline{v}}_T^2/{\Lambda}^2\left(16{\pi}^2\right)\right) $$ $O\left({\overline{v}}_T^2/{\Lambda }^2\left(16{\pi }^2\right)\right)$in the limit where subleadingm_Ψ→ 0 corrections are neglected. We clarify how gauge invariant SMEFT renormalization counterterms combine with the Standard Model counter terms in higher order SMEFT calculations when the Background Field Method is used. We also update the prediction of the total Higgs width in the SMEFT to consistently include some of these higher order perturbative effects. 

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3. Measurement of the e+e− → $$ {B}_s^0{\overline{B}}_s^0X $$ cross section in the energy range from 10.63 to 11.02 GeV using inclusive $$ {D}_s^{+} $$ and D0 production

   https://doi.org/10.1007/JHEP08(2023)131  

   Zhukova, V; Mizuk, R; Adachi, I; Aihara, H; Al_Said, S; Asner, D M; Atmacan, H; Aulchenko, V; Aushev, T; Ayad, R; et al (August 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We report the first measurement of the inclusivee⁺e⁻→$$ b\overline{b} $$ $b\overline{b}$→$$ {D}_s^{\pm } $$ $D_s^{\pm }$Xande⁺e⁻→$$ b\overline{b} $$ $b\overline{b}$→ D⁰/$$ {\overline{D}}^0 $$ ${\overline{D}}^0$Xcross sections in the energy range from 10.63 to 11.02 GeV. Based on these results, we determineσ(e⁺e⁻→$$ {B}_s^0{\overline{B}}_s^0 $$ $B_s^0{\overline{B}}_s^0$X) andσ(e⁺e⁻→$$ B\overline{B} $$ $B\overline{B}$X) in the same energy range. We measure the fraction of$$ {B}_s^0 $$ $B_s^0$events at Υ(10860) to bef_s= ($$ {22.0}_{-2.1}^{+2.0} $$ ${22.0}_{-2.1}^{+2.0}$)%. We determine also the ratio of the$$ {B}_s^0 $$ $B_s^0$inclusive branching fractions$$ \mathcal{B} $$ $B$($$ {B}_s^0 $$ $B_s^0$→ D⁰/$$ {\overline{D}}^0 $$ ${\overline{D}}^0$X)/$$ \mathcal{B} $$ $B$($$ {B}_s^0 $$ $B_s^0$→$$ {D}_s^{\pm } $$ $D_s^{\pm }$X) = 0.416 ± 0.018 ± 0.092. The results are obtained using the data collected with the Belle detector at the KEKB asymmetric-energye⁺e⁻collider. 

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4. The half-volume spectrum of a manifold

   https://doi.org/10.1007/s00526-025-02949-z  

   Mazurowski, Liam; Zhou, Xin (May 2025, Calculus of Variations and Partial Differential Equations)

   Abstract We define the half-volume spectrum$$\{{\tilde{\omega }_p\}_{p\in \mathbb {N}}}$$ $\{{\tilde{\omega }}_p{\}}_{p\in N}$of a closed manifold$$(M^{n+1},g)$$ $(M^{n+1},g)$. This is analogous to the usual volume spectrum ofM, except that we restrict top-sweepouts whose slices each enclose half the volume ofM. We prove that the Weyl law continues to hold for the half-volume spectrum. We define an analogous half-volume spectrum$$\tilde{c}(p)$$ $\tilde{c}\left(p\right)$in the phase transition setting. Moreover, for$$3 \le n+1 \le 7$$ $3\le n+1\le 7$, we use the Allen–Cahn min-max theory to show that each$$\tilde{c}(p)$$ $\tilde{c}\left(p\right)$is achieved by a constant mean curvature surface enclosing half the volume ofMplus a (possibly empty) collection of minimal surfaces with even multiplicities. 

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5. Torsion phenomena for zero-cycles on a product of curves over a number field

   https://doi.org/10.1007/s40993-024-00519-4  

   Gazaki, Evangelia; Love, Jonathan (March 2024, Research in Number Theory)

   Abstract For a smooth projective varietyXover an algebraic number fieldka conjecture of Bloch and Beilinson predicts that the kernel of the Albanese map ofXis a torsion group. In this article we consider a product$$X=C_1\times \cdots \times C_d$$ $X=C_1\times \cdots \times C_d$of smooth projective curves and show that if the conjecture is true for any subproduct of two curves, then it is true forX. For a product$$X=C_1\times C_2$$ $X=C_1\times C_2$of two curves over$$\mathbb {Q} $$ $Q$with positive genus we construct many nontrivial examples that satisfy the weaker property that the image of the natural map$$J_1(\mathbb {Q})\otimes J_2(\mathbb {Q})\xrightarrow {\varepsilon }{{\,\textrm{CH}\,}}_0(C_1\times C_2)$$ $J_1\left(Q\right)\otimes J_2\left(Q\right)\stackrel{\epsilon }{\to }{\text{CH}}_0(C_1\times C_2)$is finite, where$$J_i$$ $J_i$is the Jacobian variety of$$C_i$$ $C_i$. Our constructions include many new examples of non-isogenous pairs of elliptic curves$$E_1, E_2$$ $E_1,E_2$with positive rank, including the first known examples of rank greater than 1. Combining these constructions with our previous result, we obtain infinitely many nontrivial products$$X=C_1\times \cdots \times C_d$$ $X=C_1\times \cdots \times C_d$for which the analogous map$$\varepsilon $$ $\epsilon$has finite image. 

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