Del Pezzo surfaces with irregularity and intersection numbers on quotients in geometric invariant theory

This thesis comprises two parts covering distinct topics in algebraic geometry. In Part I, we construct the first examples of regular del Pezzo surfaces for which the first cohomology group of the structure sheaf is nonzero. Such surfaces, which only exist over imperfect fields, arise as generic fibres of fibrations of singular del Pezzo surfaces in positive characteristic whose total spaces are smooth, and their study is motivated by the minimal model program. We also find a restriction on the integer pairs that are possible as the irregularity (that is, the dimension of the first cohomology group of the structure sheaf) and anti-canonical degree of regular del Pezzo surfaces with positive irregularity. In Part II, we consider a connected reductive group acting linearly on a projective variety over an arbitrary field. We prove a formula that compares intersection numbers on the geometric invariant theory quotient of the variety by the reductive group with intersection numbers on the geometric invariant theory quotient of the variety by a maximal torus, in the case where all semi-stable points are properly stable. These latter intersection numbers involve the top equivariant Chern class of the maximal torus representation given by the quotient of the adjoint representation on the Lie algebra of the reductive group by that of the maximal torus. We provide a purely algebraic proof of the formula when the root system decomposes into irreducible root systems of type A. We are able to remove this restriction on root systems by applying a related result of Shaun Martin from symplectic geometry

Study of prompt D0^{0} meson production in ppPb collisions at sNN=5 \sqrt{s_{\mathrm{NN}}}=5 TeV

International audienceProduction of prompt D$^{0}$ mesons is studied in proton-lead and lead-proton collisions recorded at the LHCb detector at the LHC. The data sample corresponds to an integrated luminosity of 1.58±0.02 nb$^{−1}$ recorded at a nucleon-nucleon centre-of-mass energy of $\sqrt{s_{\mathrm{NN}}}=5$ TeV. Measurements of the differential cross-section, the forward-backward production ratio and the nuclear modification factor are reported using D$^{0}$ candidates with transverse momenta less than 10 GeV/c and rapidities in the ranges 1.5 < y$^{∗}$ < 4.0 and −5.0 < y$^{∗}$ < −2.5 in the nucleon-nucleon centre-of-mass system

Measurement of the shape of the Λb0→Λc+μ−ν‾μ\Lambda_b^0\to\Lambda_c^+ \mu^- \overline{\nu}_{\mu} differential decay rate

International audienceA measurement of the shape of the differential decay rate and the associated Isgur-Wise function for the decay Λb0→Λc+μ-ν¯μ is reported, using data corresponding to 3  fb-1 collected with the LHCb detector in proton-proton collisions. The Λc+μ-ν¯μ(+anything) final states are reconstructed through the detection of a muon and a Λc+ baryon decaying into pK-π+, and the decays Λb0→Λc+π+π-μ-ν¯μ are used to determine contributions from Λb0→Λc*+μ-ν¯μ decays. The measured dependence of the differential decay rate upon the squared four-momentum transfer between the heavy baryons, q2, is compared with expectations from heavy-quark effective theory and from unquenched lattice QCD predictions