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Register a new userThe Kodaira dimensions of $overline{mathcal{M}}_{22}$ and $overline{mathcal{M}}_{23}$
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We prove that the moduli spaces of curves of genus 22 and 23 are of general type. To do this, we calculate certain virtual divisor classes of small slope associated to linear series of rank 6 with quadric relations. We then develop new tropical methods for studying linear series and independence of quadrics and show that these virtual classes are represented by effective divisors.
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We study smoothing of pencils of curves on surfaces with normal crossings. As a consequence we show that the canonical divisor of $overline{mathcal{M}}_{g,n}$ is not pseudo-effective in some range, implying that $overline{mathcal{M}}_{12,6},overline{mathcal{M}}_{12,7},overline{mathcal{M}}_{13,4}$ and $overline{mathcal{M}}_{14,3}$ are uniruled. We provide upper bounds for the Kodaira dimension of $overline{mathcal{M}}_{12,8}$ and $overline{mathcal{M}}_{16}$. We also show that the moduli of $(4g+5)$-pointed hyperelliptic curves $mathcal{H}_{g,4g+5}$ is uniruled. Together with a recent result of Schwarz, this concludes the Kodaira classification for moduli of pointed hyperelliptic curves.
We extend HPQCDs earlier $n_f=4$ lattice-QCD analysis of the ratio of $overline{mathrm{MSB}}$ masses of the $b$ and $c$ quark to include results from finer lattices (down to 0.03fm) and a new calculation of QED contributions to the mass ratio. We find that $overline{m}_b(mu)/overline{m}_c(mu)=4.586(12)$ at renormalization scale $mu=3$,GeV. This result is nonperturbative. Combining it with HPQCDs recent lattice QCD$+$QED determination of $overline{m}_c(3mathrm{GeV})$ gives a new value for the $b$-quark mass: $overline{m}_b(3mathrm{GeV}) = 4.513(26)$GeV. The $b$-mass corresponds to $overline{m}_b(overline{m}_b, n_f=5) = 4.202(21)$GeV. These results are the first based on simulations that include QED.
We determine five extremal effective rays of the four-dimensional cone of effective surfaces on the toroidal compactification $overline{mathcal A}_3$ of the moduli space ${mathcal A}_3$ of complex principally polarized abelian threefolds, and we conjecture that the cone of effective surfaces is generated by these surfaces. As the surfaces we define can be defined in any genus $gge 3$, we further conjecture that they generate the cone of effective surfaces on the perfect cone toroidal compactification of ${mathcal A}_g$ for any $gge 3$.
In this work we study the tau-function $Z^{1D}$ of the KP hierarchy specified by the topological 1D gravity. As an application, we present two types of algorithms to compute the orbifold Euler characteristics of $overline{mathcal M}_{g,n}$. The first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for $Z^{1D}$; and the second is to use a formula for the connected $n$-point functions of a KP tau-function in terms of its affine coordinates on the Sato Grassmannian. This is a sequel to an earlier work.
The branching fraction ratio $mathcal{R}(D^{*}) equiv mathcal{B}(overline{B}^0 to D^{*+}tau^{-}overline{ u}_{tau})/mathcal{B}(overline{B}^0 to D^{*+}mu^{-}overline{ u}_{mu})$ is measured using a sample of proton-proton collision data corresponding to 3.0invfb of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode $tau^{-} to mu^{-}overline{ u}_{mu} u_{tau}$. The semitauonic decay is sensitive to contributions from non-Standard-Model particles that preferentially couple to the third generation of fermions, in particular Higgs-like charged scalars. A multidimensional fit to kinematic distributions of the candidate $overline{B}^0$ decays gives $mathcal{R}(D^{*}) = 0.336 pm 0.027(stat) pm 0.030 (syst)$. This result, which is the first measurement of this quantity at a hadron collider, is $2.1$ standard deviations larger than the value expected from lepton universality in the Standard Model.
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