scholarly journals K3 curves with index $$k>1$$

2021 ◽  
Author(s):  
Ciro Ciliberto ◽  
Thomas Dedieu
Keyword(s):  
Complete Intersection ◽  
Fano Varieties ◽  
Canonical Embedding ◽  
Geometric Means ◽  
Moduli Stack

AbstractLet $$\mathcal {KC}_g ^k$$ KC g k be the moduli stack of pairs (S, C) with S a K3 surface and $$C\subseteq S$$ C ⊆ S a genus g curve with divisibility k in $$\mathrm {Pic}(S)$$ Pic ( S ) . In this article we study the forgetful map $$c_g^k:(S,C) \mapsto C$$ c g k : ( S , C ) ↦ C from $$\mathcal {KC}_g ^k$$ KC g k to $${\mathcal {M}}_g$$ M g for $$k>1$$ k > 1 . First we compute by geometric means the dimension of its general fibre. This turns out to be interesting only when S is a complete intersection or a section of a Mukai variety. In the former case we find the existence of interesting Fano varieties extending C in its canonical embedding. In the latter case this is related to delicate modular properties of the Mukai varieties. Next we investigate whether $$c_g^k$$ c g k dominates the locus in $${\mathcal {M}}_g$$ M g of k-spin curves with the appropriate number of independent sections. We are able to do this only when S is a complete intersection, and obtain in these cases some classification results for spin curves.

Estimation of geographical variation of cancer risks in drinking water in Japan

2006 ◽  
Vol 6 (2) ◽  
pp. 31-37
Author(s):  
K. Ohno ◽  
E. Kadota ◽  
Y. Kondo ◽  
T. Kamei ◽  
Y. Magara
Keyword(s):  
Geographical Variation ◽  
Statistical Data ◽  
Raw Water ◽  
Cancer Risks ◽  
Geometric Means ◽  
Toxicological Effects ◽  
Total Cancer ◽  
Big Cities ◽  
The Relationship ◽  
Plausible Reason

The cancer risks posed by ten substances in raw and purified water were estimated for each municipality in Japan to compare risks between raw and purified water, and inter-municipality. Water concentrations were estimated by use of statistical data. Assigning cancer unit risks to each substance and applying the assumption of additive toxicological effects to multiple carcinogens, total cancer risks of the waters were estimated. As a result, the geometric means of total cancer risks in raw and purified water were 1.16×10−5 and 2.18×10−5, respectively. In raw water, the contribution ratio of arsenic to total cancer risk accounted for 97%. In purified water, that of four trihalomethanes (THMs) accounted for 54%. The increase of total cancer risks in purified water was due to THMs. In regard to the geographical variation, the relationship between population size and total cancer risks were investigated. The result was that there were higher cancer risks in the big cities with the population more than a million both in raw and purified water. One plausible reason for the higher risks in purified water in the big cities is a larger chlorination dose due to the huge water supply areas. The reason for the increase in raw water remained unclear.

scholarly journals Multiplicative Chow–Künneth decompositions and varieties of cohomological K3 type

2021 ◽  
Author(s):  
Lie Fu ◽  
Robert Laterveer ◽  
Charles Vial
Keyword(s):  
Projective Variety ◽  
Arbitrary Dimension ◽  
Smooth Projective Variety ◽  
The Other ◽  
Fano Variety ◽  
Fano Varieties ◽  
Intersection Product ◽  
Canonical Class ◽  
Main Input

AbstractGiven a smooth projective variety, a Chow–Künneth decomposition is called multiplicative if it is compatible with the intersection product. Following works of Beauville and Voisin, Shen and Vial conjectured that hyper-Kähler varieties admit a multiplicative Chow–Künneth decomposition. In this paper, based on the mysterious link between Fano varieties with cohomology of K3 type and hyper-Kähler varieties, we ask whether Fano varieties with cohomology of K3 type also admit a multiplicative Chow–Künneth decomposition, and provide evidence by establishing their existence for cubic fourfolds and Küchle fourfolds of type c7. The main input in the cubic hypersurface case is the Franchetta property for the square of the Fano variety of lines; this was established in our earlier work in the fourfold case and is generalized here to arbitrary dimension. On the other end of the spectrum, we also give evidence that varieties with ample canonical class and with cohomology of K3 type might admit a multiplicative Chow–Künneth decomposition, by establishing this for two families of Todorov surfaces.

scholarly journals On the Hodge conjecture for quasi-smooth intersections in toric varieties

2021 ◽  
Author(s):  
Ugo Bruzzo ◽  
William Montoya
Keyword(s):  
Complete Intersection ◽  
Toric Variety ◽  
Toric Varieties ◽  
Picard Group ◽  
Hodge Conjecture ◽  
Smooth Hypersurface ◽  
Suitable Notion

AbstractWe establish the Hodge conjecture for some subvarieties of a class of toric varieties. First we study quasi-smooth intersections in a projective simplicial toric variety, which is a suitable notion to generalize smooth complete intersection subvarieties in the toric environment, and in particular quasi-smooth hypersurfaces. We show that under appropriate conditions, the Hodge conjecture holds for a very general quasi-smooth intersection subvariety, generalizing the work on quasi-smooth hypersurfaces of the first author and Grassi in Bruzzo and Grassi (Commun Anal Geom 28: 1773–1786, 2020). We also show that the Hodge Conjecture holds asymptotically for suitable quasi-smooth hypersurface in the Noether–Lefschetz locus, where “asymptotically” means that the degree of the hypersurface is big enough, under the assumption that the ambient variety $${{\mathbb {P}}}_\Sigma ^{2k+1}$$ P Σ 2 k + 1 has Picard group $${\mathbb {Z}}$$ Z . This extends to a class of toric varieties Otwinowska’s result in Otwinowska (J Alg Geom 12: 307–320, 2003).

scholarly journals On properness of K-moduli spaces and optimal degenerations of Fano varieties

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Harold Blum ◽  
Daniel Halpern-Leistner ◽  
Yuchen Liu ◽  
Chenyang Xu
Keyword(s):  
Moduli Spaces ◽  
Fano Varieties

scholarly journals Betti numbers and pseudoeffective cones in 2-Fano varieties

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Giosuè Emanuele Muratore
Keyword(s):  
Large Class ◽  
Betti Numbers ◽  
Fano Varieties ◽  
Higher Dimensional ◽  
Special Case ◽  
Answering Questions

Abstract The 2-Fano varieties, defined by De Jong and Starr, satisfy some higher-dimensional analogous properties of Fano varieties. We consider (weak) k-Fano varieties and conjecture the polyhedrality of the cone of pseudoeffective k-cycles for those varieties, in analogy with the case k = 1. Then we calculate some Betti numbers of a large class of k-Fano varieties to prove some special case of the conjecture. In particular, the conjecture is true for all 2-Fano varieties of index at least n − 2, and we complete the classification of weak 2-Fano varieties answering Questions 39 and 41 in [2].

scholarly journals Heterotic line bundle models on generalized complete intersection Calabi Yau manifolds

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Magdalena Larfors ◽  
Davide Passaro ◽  
Robin Schneider
Keyword(s):  
Line Bundle ◽  
Complete Intersection ◽  
Particle Physics ◽  
Model Building ◽  
Wilson Line ◽  
Symmetry Groups ◽  
The Standard Model ◽  
Order Of Magnitude ◽  
Systematic Program ◽  
Calabi Yau Manifolds

Abstract The systematic program of heterotic line bundle model building has resulted in a wealth of standard-like models (SLM) for particle physics. In this paper, we continue this work in the setting of generalised Complete Intersection Calabi Yau (gCICY) manifolds. Using the gCICYs constructed in ref. [1], we identify two geometries that, when combined with line bundle sums, are directly suitable for heterotic GUT models. We then show that these gCICYs admit freely acting ℤ2 symmetry groups, and are thus amenable to Wilson line breaking of the GUT gauge group to that of the standard model. We proceed to a systematic scan over line bundle sums over these geometries, that result in 99 and 33 SLMs, respectively. For the first class of models, our results may be compared to line bundle models on homotopically equivalent Complete Intersection Calabi Yau manifolds. This shows that the number of realistic configurations is of the same order of magnitude.

Microbiological Quality of Fresh Blue Crabmeat, Clams and Oysters

1983 ◽  
Vol 46 (11) ◽  
pp. 978-981 ◽  
Author(s):  
B. A. WENTZ ◽  
A. P. DURAN ◽  
A. SWARTZENTRUBER ◽  
A. H. SCHWAB ◽  
R. B. READ
Keyword(s):  
Escherichia Coli ◽  
Staphylococcus Aureus ◽  
Microbiological Quality ◽  
Fecal Coliforms ◽  
Geometric Means ◽  
Colony Forming Units ◽  
Plate Counts ◽  
The Mean ◽  
Eastern Oysters

The microbiological quality of fresh blue crabmeat, soft- and hardshell clams and shucked Eastern oysters was determined at the retail (crabmeat, oysters) and wholesale (clams) levels. Geometric means of aerobic plate counts incubated at 35°C were: blue crabmeat 140,000 colony-forming units (CFU)/g, hardshell clams, 950 CFU/g, softshell clams 680 CFU/g and shucked Eastern oysters 390,000 CFU/g. Coliform geometric means ranged from 3,6/100 g for hardshell clams to 21/g for blue crabmeat. Means for fecal coliforms or Escherichia coli ranged from <3/100 g for clams to 27/100 g for oysters, The mean Staphylococcus aureus count in blue crabmeat was 10/g.

scholarly journals Ulrich Bundles on Intersections of Two 4-Dimensional Quadrics

2019 ◽  
Author(s):  
Yonghwa Cho ◽  
Yeongrak Kim ◽  
Kyoung-Seog Lee
Keyword(s):  
Complete Intersection ◽  
Moduli Space ◽  
Main Ingredient ◽  
Categorical Methods

Abstract In this paper, we investigate the moduli space of Ulrich bundles on a smooth complete intersection of two $4$-dimensional quadrics in $\mathbb P^5$. The main ingredient is the semiorthogonal decomposition by Bondal–Orlov, combined with the categorical methods pioneered by Kuznetsov and Lahoz–Macrì–Stellari. Using these methods, we prove that any smooth intersection of two 4-dimensional quadrics in $\mathbb P^5$ carries an Ulrich bundle of rank $r$ for every $r \ge 2$. Moreover, we provide a description of the moduli space of stable Ulrich bundles.

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