Discrepancies of non-\Q-Gorenstein varieties

We give an example of a non \Q-Gorenstein variety which is canonical but not klt, and whose canonical divisor has an irrational valuation. We also give an example of an irrational jumping number and we prove that there are no accumulation points for the jumping numbers of normal non-\Q-Gorenstein varieties with isolated singularities.Comment: 12 pages - minor change

A note on the birational geometry of tropical line bundles

Given a closed subvariety Y of a n-dimensional torus, we study how the tropical line bundles of Trop(Y) can be induced by line bundles living on a tropical compactification of Y in a toric variety, following the construction of Jenia Tevelev. We then consider the general structure with respect to the Zariski--Riemann space.Comment: Version

Ample Weil divisors

We define and study positivity (nefness, amplitude, bigness and pseudo-effectiveness) for Weil divisors on normal projective varieties. We prove various characterizations, vanishing and non-vanishing theorems for cohomology, global generation statements, and a result related to log Fano.Comment: Version 3: published versio

On positivity and base loci of vector bundles

The aim of this note is to shed some light on the relationships among some notions of positivity for vector bundles that arose in recent decades. Our purpose is to study several of the positivity notions studied for vector bundles with some notions of asymptotic base loci that can be defined on the variety itself, rather than on the projectivization of the given vector bundle. We relate some of the different notions conjectured to be equivalent with the help of these base loci, and we show that these can help simplify the various relationships between the positivity properties present in the literature. In particular, we define augmented and restricted base loci $\mathbb{B}_+ (E)$ and $\mathbb{B}_- (E)$ of a vector bundle $E$ on the variety $X$, as generalizations of the corresponding notions studied extensively for line bundles. As it turns out, the asymptotic base loci defined here behave well with respect to the natural map induced by the projectivization of the vector bundle $E$

MODIFIKASI KITOSAN MAKROPORI TERTAUTSILANG BADGE (BISPHENOL A DIGLYCIDYL ETHER) DENGAN POROGEN NaCl SEBAGAI ADSORBEN ZAT WARNA PROCION RED MX 8B

Penelitian tentang modifikasi kitosan makropori yang tertautsilang bisphenol A diglycidyl ether (BADGE) dengan porogen NaCl (CTS-M-BADGE) sebagai adsorben zat warna Procion Red MX 8B (PR MX 8B) telah berhasil dilakukan. Kajian adsorpsi yang dipelajari meliputi pengaruh keasaman media, model kinetika dan isoterm adsorpsi pada sistem batch. Adsorben CTS-M-BADGE disintesis melalui empat tahap yaitu pencampuran larutan kitosan dengan NaCl, kroslingking dengan BADGE, pengeringan dan tahap akhirnya adalah pelarutan porogen NaCl dengan menggunakan akuades guna membentuk rongga pori. Karakterisasi CTS-MBADGE dilakukan dengan menggunakan FTIR dan SEM. Spektra FTIR menunjukkan puncak baru pada 833,25 cm-1 (-CH benzena tersubstitusi para), 1512,19 cm-1 (vibrasi ulur C=C dari cincin aromatis) yang merupakan karakteristik dari BADGE dan pergeseran panjang gelombang dari 1651,07 cm-1 menjadi 1604,77 cm-1 mengindikasikan berkurangnya gugus amina primer akibat berikatan dengan BADGE. Hasil SEM memperlihatkan bahwa CTS-M-BADGE memiliki pori yang besar dibandingkan kitosan. Hasil penelitian menunjukkan kondisi optimum adsorpsi zat warna PR MX 8B pada adsorben CTS-M-BADGE terjadi pada pH 3 dengan waktu kontak 60 menit. Adsorpsi zat warna PR MX 8B oleh CTS-M-BADGE mengikuti kinetika pseudo-orde dua dengan konstanta laju adsorpsi 42,65 x 10-2 mg-1 menit-1. Kajian isoterm adsorpsi mengikuti model isoterm Freundlich dengan kapasitas adsorpsi sebesar 148,609 mg/g