Singular del Pezzo fibrations and birational rigidity

A known conjecture of Grinenko in birational geometry asserts that a Mori fibre space with the structure of del Pezzo fibration of low degree is birationally rigid if and only if its anticanonical class is an interior point in the cone of mobile divisors. The conjecture is proved to be true for smooth models (with a generality assumption for degree 3). It is speculated that the conjecture holds for, at least, Gorenstein models in degree 1 and 2. In this article, I present a (Gorenstein) counterexample in degree 2 to this conjecture.Comment: This is essentially a more detailed version of the second section of arXiv:1310.5548. To appear in the proceedings of the conference 'Groups of Automorphisms in Birational and Affine Geometry', held in Trento, Italy, 201

Non-rigid quartic 3-folds

Let X C P4 be a terminal factorial quartic 3-fold. If X is non-singular, X is birationally rigid, i.e. the classical minimal model program on any terminal Q-factorial projective variety Z birational to X always terminates with X. This no longer holds when X is singular, but very few examples of non-rigid factorial quartics are known. In this article, we first bound the local analytic type of singularities that may occur on a terminal factorial quartic hypersurface X c P4. A singular point on such a hypersurface is either of type cAn (n > or equal 1), or of type cDm (m> or equal 4), or of type cE6, cE7 or cE8. We first show that if (P e X) is of type cAn, n is at most 7, and if (P \in X) is of type cDm, m is at most 8. We then construct examples of non-rigid factorial quartic hypersurfaces whose singular loci consist (a) of a single point of type cAn for 2\leq n\leq 7 (b) of a single point of type cDm for m= 4 or 5 and (c) of a single point of type cEk for k=6,7 or 8

Fano 3-folds in P2xP2 format, Tom and Jerry

We study Q-factorial terminal Fano 3-folds whose equations are modelled on those of the Segre embedding of P^2xP^2. These lie in codimension 4 in their total anticanonical embedding and have Picard rank 2. They fit into the current state of classification in three different ways. Some families arise as unprojections of degenerations of complete intersections, where the generic unprojection is a known prime Fano 3-fold in codimension 3; these are new, and an analysis of their Gorenstein projections reveals yet other new families. Others represent the "second Tom" unprojection families already known in codimension 4, and we show that every such family contains one of our models. Yet others have no easy Gorenstein projection analysis at all, so prove the existence of Fano components on their Hilbert scheme

Determination of optimum dosage of Ovaprim injectionon artificial spawning efficiency of Esox lucius

This project was conducted to goal of optimum dosage determination of ovaprim injection to artificial spawning efficiency of Esox lucius. The research implemented by 4 treatments with 3 replicates for each ones. 3 female and 6 male brooders injected in each replicate. The animals in 1, 2 and 3 treatments injected by 10, 20 and 30 µg/kg BW, respectively, and 4th treatment as a control injected with 4 mg/kg BW pituitary gland extract. Average weight of brooders were 1361±521, 1376±954, 1009±160 and 1100 ±422 g in 1, 2, 3 and 4 treatments in females and 689±145, 734±197, 547±118 and 794±238 g in males, respectively. In addition, positive response percent to hormone injection were measured 77.8 ±19.24 , 88.9 ± 19.24 , 55.5 ±50.91 and 55.5 ± 19.24 % in 1, 2, 3 and 4 treatments in female and 94.4 ± 9.58, 88.9 ±19.26 , 83.3±28.86 and 88.9 ± 19.26 % in male brooders, respectively, but there was no significant different between all of treatments (p<0.05). Incubation period from fertilization till hatching step in 7 to 15 ˚C was 5 to 10 days with average of 7±1.5 days. Fertilization content was in 1 to 4 treatments measured 87.1±10, 88.04±7.7, 83.9±5.2 and 72.4±19.7 %, respectively and also the treatments didn’t show any different significantly together (p<0.05). Average percentage of eyed eggs 66.6±15.9 in treat 1, 61.2±22.3 in treat 2, 58.3±10.7 in treat 3 and 56.1±15.04 in treat 4, without any significant different between of them (p<0.05). Hatching of eggs mean were measured 27.41±19.8 in treat 1, 39.53±26.9 in treat 2, 95.18±5.6 in treat 3 and 26.78±12.4 in treat 4, and significant different observed between of them too (p<0.05).In the other hand, mean percent of larvae with active feeding in these treatments were measured 18.77±14.6, 20.1±8.51, 55.6±11.6 and 14.51±7.72 as the treatments had significant different (p<0.05). Also, the best temperature and dosage injection of ovaprim hormone was 9 to 12.5 ˚C and 20µg/kg BW, respectively. The end of trial, from 103740 larvae introduced to earthen pond obtained 8000 fingerlings with weight of 2.68±0.6 g and length of 6.96±0.51 cm