Local Fano-Mori contractions of high nef-value

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Fano-Mori contractions of high length on projective varieties with terminal singularities

Let X be a projective variety with terminal singularities and let L be an ample Cartier divisor on X. We prove that if f is a birational contraction associated to an extremal ray $R \subset \bar {NE(X)}$ such that R.(K_X+(n-2)L)<0, then f is a weighted blow-up of a smooth point. We then classify divisorial contractions associated to extremal rays R such that R.(K_X+rL)<0, where r is a non-negative rational number, and the fibres of f have dimension less or equal to r+1.Comment: 12 pages. We fixed some lemmas and improved the exposition. To appear in the Bulletin of the London Mathematical Societ

Algebraic structures with unbounded Chern numbers

We determine all Chern numbers of smooth complex projective varieties of dimension at least four which are determined up to finite ambiguity by the underlying smooth manifold. We also give an upper bound on the dimension of the space of linear combinations of Chern numbers with that property and prove its optimality in dimension four.Comment: 15 pages; final version, to appear in Journal of Topolog

On some modular contractions of the moduli space of stable pointed curves

The aim of this paper is to study some modular contractions of the moduli space of stable pointed curves. These new moduli spaces, which are modular compactifications of the moduli space of smooth pointed curves, are related with the minimal model program for the moduli space of stable pointed curves and have been introduced in a previous work of the authors. We interpret them as log canonical models of adjoints divisors and we then describe the Shokurov decomposition of a region of boundary divisors on the moduli space of stable pointed curves.Comment: 30 pages, 1 figure. To appear on Algebra and Number Theor

Effective non-vanishing for Fano weighted complete intersections

We show that Ambro-Kawamata's non-vanishing conjecture holds true for a quasi-smooth WCI X which is Fano or Calabi-Yau, i.e. we prove that, if H is an ample Cartier divisor on X, then |H| is not empty. If X is smooth, we further show that the general element of |H| is smooth. We then verify Ambro-Kawamata's conjecture for any quasi-smooth weighted hypersurface. We also verify Fujita's freeness conjecture for a Gorenstein quasi-smooth weighted hypersurface. For the proofs, we introduce the arithmetic notion of regular pairs and enlighten some interesting connection with the Frobenius coin problem.Comment: 27 pages. Revised version to appear in Algebra and Number Theor

A remark on the Ueno-Campana's threefold

We show that the Ueno-Campana's threefold cannot be obtained as the blow-up of any smooth threefold along a smooth centre, answering negatively a question raised by Oguiso and Truong.Comment: To appear on Michigan Math. Journal, Vol. 65 (2016

Factors Influecing Customer's Trust in Online Shopping Among Executives in a Bank

Having many advantages that traditional shopping lack of, online shopping is now enjoying its predominance and rapid development in Malaysia. In many previous researches, focus has been found in the relationship between consumer trust and its antecedents. The objective of this study is to examine some factors affecting consumer trust in Malaysia as well as to investigate the relationship between trust and purchasing decision. A questionnaire was distributed among bank employees of CIMB Bank Berhad. Correlations and regressions were used in analyzing the data. This paper provides evidence that trust in online shopping is built on information quality, online consumer review and site quality. It also proves that trust contributes to the online purchasing decision

On the Chern numbers of a smooth threefold

We study the behaviour of Chern numbers of three dimensional terminal varieties under divisorial contractions.Comment: 41 pages. Revised version, to appear in Trans. Amer. Math. So