Generalized Lazarsfeld-Mukai bundles and a conjecture of Donagi and Morrison

Let S be a K3 surface and assume for simplicity that it does not contain any (-2)-curve. Using coherent systems, we express every non-simple Lazarsfeld-Mukai bundle on S as an extension of two sheaves of some special type, that we refer to as generalized Lazarsfeld-Mukai bundles. This has interesting consequences concerning the Brill-Noether theory of curves C lying on S. From now on, let g denote the genus of C and A be a complete linear series of type g^r_d on C such that d<= g-1 and the corresponding Brill-Noether number is negative. First, we focus on the cases where A computes the Clifford index; if r>1 and with only some completely classified exceptions, we show that A coincides with the restriction to C of a line bundle on S. This is a refinement of Green and Lazarsfeld's result on the constancy of the Clifford index of curves moving in the same linear system. Then, we study a conjecture of Donagi and Morrison predicting that, under no hypothesis on its Clifford index, A is contained in a g^s_e which is cut out from a line bundle on S and satisfies e<= g-1. We provide counterexamples to the last inequality already for r=2. A slight modification of the conjecture, which holds for r=1,2, is proved under some hypotheses on the pair (C,A) and its deformations. We show that the result is optimal (in the sense that our hypotheses cannot be avoided) by exhibiting, in the Appendix, some counterexamples obtained jointly with Andreas Leopold Knutsen.Comment: 28 pages, final version, to appear in Adv. Math. with an Appendix joint with Andreas Leopold Knutse

STRATEGI PEMASARAN PRODUK TABUNGAN EMAS PADA PT. PEGADAIAN CABANG SIDOARJO

The purpose of this scientific study is to identify the promotional mix for gold savings services at the Sidoarjo branch of the pawnshop. The result of this study explain the promotional mix of PT Pegadaian Sidoarjo branch. The existence of promotion shows that the market potential for gold savings product is very large, but public awareness about the benefits of gold savings is still low. The conclusionof this research is that promotional strategy is an important key in increasing brand awareness and collaborating with influencers in the financial sector to provide positive testimonals about gold savings produc

Phases of attractive spin-imbalanced fermions in square lattices

We determine the relative stability of different ground-state phases of spin-imbalanced popula- tions of attractive fermions in square lattices. The phases are systematically characterized by the symmetry of the order parameter and the real- and momentum-space structures using Hartree- Fock-Bogoliubov theory. We find several type of unidirectional Larkin-Ovchinikov-type phases. We discuss the effect of commensuration between the ordering wave vector and the density imbalance, and describe the mechanism of Fermi surface reconstruction and pairing for various orders. A robust supersolid phase is shown to exist when the ordering wave vector is diagonally directed.Comment: 6.5 pages, 5 figure