NORMAL ALGEBRAIC SURFACES WITH TRIVIAL TWO OR FOUR TIMES OF THE CANONICAL DIVISOR

1998 ◽  
Vol 09 (03) ◽  
pp. 377-406
Author(s):  
D.-Q. ZHANG
Keyword(s):  
Type A ◽  
Algebraic Surfaces ◽  
Enriques Surface ◽  
Canonical Divisor ◽  
Enriques Surfaces ◽  
Actual Type

We prove that upto isomorphisms there are exactly, three rational log Enriques surface of index four and Type A17, and three rational log Enriques surfaces of index two and actual Type A17 + A1.

scholarly journals Rank one sheaves over quaternion algebras on Enriques surfaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Fabian Reede
Keyword(s):  
Quaternion Algebra ◽  
Double Cover ◽  
Complex Numbers ◽  
K3 Surface ◽  
Enriques Surface ◽  
Quaternion Algebras ◽  
Enriques Surfaces ◽  
Rank One ◽  
Torsion Free

Abstract Let X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra 𝓐 on X. Then we study the moduli scheme of torsion free 𝓐-modules of rank one. Finally we prove that this moduli scheme is an étale double cover of a Lagrangian subscheme in the corresponding moduli scheme on the associated covering K3 surface.

scholarly journals Moduli spaces of stable vector bundles on Enriques surfaces

1998 ◽  
Vol 150 ◽  
pp. 85-94 ◽  
Author(s):  
Hoil Kim
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
K3 Surface ◽  
Enriques Surface ◽  
Stable Bundles ◽  
Stable Vector Bundles ◽  
Enriques Surfaces

Abstract.We show that the image of the moduli space of stable bundles on an Enriques surface by the pull back map is a Lagrangian subvariety in the moduli space of stable bundles, which is a symplectic variety, on the covering K3 surface. We also describe singularities and some other features of it.

scholarly journals Arithmetic moduli and lifting of Enriques surfaces

2015 ◽  
Vol 2015 (706) ◽  
Author(s):  
Christian Liedtke
Keyword(s):  
Complete Intersection ◽  
Moduli Space ◽  
Characteristic Zero ◽  
Positive Characteristic ◽  
Double Cover ◽  
Global Structure ◽  
Enriques Surface ◽  
Enriques Surfaces

AbstractWe construct the moduli space of Enriques surfaces in positive characteristic and eventually over the integers, and determine its local and global structure. As an application, we show lifting of Enriques surfaces to characteristic zero. The key observation is that the canonical double cover of an Enriques surface is birational to the complete intersection of three quadrics in ℙ

scholarly journals Twelve Rational curves on Enriques surfaces

2021 ◽  
Vol 8 (2) ◽  
Author(s):  
Sławomir Rams ◽  
Matthias Schütt
Keyword(s):  
Rational Curves ◽  
Enriques Surface ◽  
Enriques Surfaces ◽  
High Degree ◽  
Rational Degree

AbstractGiven $$d\in {\mathbb {N}}$$ d ∈ N , we prove that any polarized Enriques surface (over any field k of characteristic $$p \ne 2$$ p ≠ 2 or with a smooth K3 cover) of degree greater than $$12d^2$$ 12 d 2 contains at most 12 rational curves of degree at most d. For $$d>2$$ d > 2 , we construct examples of Enriques surfaces of high degree that contain exactly 12 rational degree-d curves.

Algebraic surfaces with nef and big anti-canonical divisor

1995 ◽  
Vol 117 (1) ◽  
pp. 161-163 ◽  
Author(s):  
D.-Q. Zhang
Keyword(s):  
Algebraic Surface ◽  
Algebraic Surfaces ◽  
Pezzo Surface ◽  
Canonical Divisor ◽  
Del Pezzo Surface ◽  
Projective Algebraic Surface ◽  
Quotient Singularities ◽  
Del Pezzo

Let S be a normal projective algebraic surface over C with at worst quotient singularities. S is a quasi-log del Pezzo surface if the anti-canonical divisor — Ks is nef (= numerically effective) and big, i.e. — Ks. C ≥ 0 for all curves C on S and (−Ks)2 > 0. Further, if — Ks is ample we say S is a log del Pezzo surface.

scholarly journals Q_l-cohomology projective planes and singular Enriques surfaces in characteristic two

2019 ◽  
Vol Volume 3 ◽  
Author(s):  
Matthias Schütt
Keyword(s):  
Projective Planes ◽  
Rational Curves ◽  
Existence Results ◽  
Algebraic Surfaces ◽  
Prime Field ◽  
One Dimensional ◽  
Enriques Surfaces ◽  
Characteristic Two ◽  
The Given ◽  
Root Types

We classify singular Enriques surfaces in characteristic two supporting a rank nine configuration of smooth rational curves. They come in one-dimensional families defined over the prime field, paralleling the situation in other characteristics, but featuring novel aspects. Contracting the given rational curves, one can derive algebraic surfaces with isolated ADE-singularities and trivial canonical bundle whose Q_l-cohomology equals that of a projective plane. Similar existence results are developed for classical Enriques surfaces. We also work out an application to integral models of Enriques surfaces (and K3 surfaces). Comment: 24 pages; v3: journal version, correcting 20 root types to 19 and ruling out the remaining type 4A_2+A_1 (in new section 11)

Biological and Morphological Studies on Low-Leukemia-Strain Mice with Hodgkin's-Like Neoplasia Induced by Serial Cell-Free Transmission of Leukemic Organs of SJL/J Strain Mice

1968 ◽  
Vol 26 ◽  
pp. 210-211
Author(s):  
S. Fujinaga ◽  
K. Maruyama ◽  
C.W. Williams ◽  
K. Sekhri ◽  
L. Dmochowski
Keyword(s):  
Tissue Culture ◽  
Type A ◽  
Reticulum Cell ◽  
Type B ◽  
Viral Origin ◽  
Serial Transfer ◽  
Strain Mouse ◽  
Morphological Studies ◽  
Cell Neoplasm ◽  
Free Material

Yumoto and Dmochowski (Cancer Res.27, 2098 (1967)) reported the presence of mature and immature type C leukemia virus particles in leukemic organs and tissues such as lymph nodes, spleen, thymus, liver, and kidneys of SJL/J strain mice with Hodgki's-like disease or reticulum cell neoplasm (type B). In an attempt to ascertain the possibility that this neoplasia may be of viral origin, experiments with induction and transmission of this neoplasm were carried out using cell-free extracts of leukemic organs from an SJL/J strain mouse with spontaneous disease.It has been possible to induce the disease in low-leukemia BALB/c and C3HZB strain mice and serially transfer the neoplasia by cell-free extracts of leukemic organs of these mice. Histological examination revealed the neoplasia to be of either reticulum cell-type A or type B. Serial transfer is now in its fifth passage. In addition leukemic spleen from another SJL/J strain mouse with spontaneous reticulum cell neoplasm (type A) was set up in tissue culture and is now in its 141st serial passage in vitro. Preliminary results indicate that cell-free material of 39th tissue culture passage can reproduce neoplasia in BALB/c mice.

Hepatitis A Antigen in Liver, Bile and Stool

1975 ◽  
Vol 33 ◽  
pp. 340-341
Author(s):  
D.R. Jackson ◽  
J.H. Hoofnagle ◽  
A.N. Schulman ◽  
J.L. Dienstag ◽  
R.H. Purcell ◽  
...  
Keyword(s):  
Hepatitis A ◽  
Liver Enzymes ◽  
Hepatitis A Virus ◽  
Type A ◽  
Initial Study ◽  
Virus Like Particle ◽  
Elevated Liver Enzymes ◽  
Ag Particles ◽  
Ag Particle ◽  
Human Stool

Using immune electron microscopy Feinstone et. al. demonstrated the presence of a 27 nm virus-like particle in acute-phase stools of patients with viral hepatitis, type A, These hepatitis A antigen (HA Ag) particles were aggregated by convalescent serum from patients with type A hepatitis but not by pre-infection serum. Subsequently Dienstag et. al. and Maynard et. al. produced acute hepatitis in chimpanzees by inoculation with human stool containing HA Ag. During the early acute disease, virus like particles antigenically, morphologically and biophysically identical to the human HA Ag particle were found in chimpanzee stool. Recently Hilleman et. al. have described similar particles in liver and serum of marmosets infected with hepatitis A virus (HAV). We have investigated liver, bile and stool from chimpanzees and marmosets experimentally infected with HAV. In an initial study, a chimpanzee (no.785) inoculated with HA Ag-containing stool developed elevated liver enzymes 21 days after exposure.

Detection of Viral Antigens in Mouse and Rat Tumor Cells by Immunoelectron Microscopy Following Periodate-Lysine-Paraformaldehyde (PLP) Fixation

1976 ◽  
Vol 34 ◽  
pp. 252-253
Author(s):  
Y. Ohtsuki ◽  
G. Seman ◽  
J. M. Bowen ◽  
M. Scanlon ◽  
L. Dmochowski
Keyword(s):  
Immunoelectron Microscopy ◽  
Mammary Tumor ◽  
Type A ◽  
Rabbit Serum ◽  
Virus Particles ◽  
Viral Antigens ◽  
Culture Cells ◽  
Mouse Mammary Tumor ◽  
Tumor Virus ◽  
Immunoperoxidase Labeling

Recently, periodate-lysine-paraformaldehyde (PLP) fixation was reported for immunoelectron microscopy (1). In PLP fixation, carbohydrates are oxidized by periodate and cross-linked by lysine; paraformaldehyde stabilizes proteins and lipids. By using PLP fixation, intracytoplasmic type A viral antigens have been previously demonstrated by immunoperoxidase labeling (2). In the present study, PLP fixation has been applied for the detection of the same antigens in mouse mammary tumor culture cells by both immunoferritin and immunoperoxidase methods. Rabbit anti-intracytoplasmic type A virus serum (anti-A), kindly provided by Dr. M. Muller (3), rabbit anti-strain A mouse mammary tumor virus (anti-MMTV) and preimmune rabbit serum as control were used to detect viral antigens in cells of C3H/HeJ strain mouse mammary tumor culture. Attempts have been also made to demonstrate peroxidase labeling of type C virus particles in frozen sections of an SD-MSV-induced NZB rat bone tumor tissue by rabbit anti-MuLV serum.

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