scholarly journals AT MOST 64 LINES ON SMOOTH QUARTIC SURFACES (CHARACTERISTIC 2)

2017 ◽  
Vol 232 ◽  
pp. 76-95
Author(s):  
SŁAWOMIR RAMS ◽  
MATTHIAS SCHÜTT
Keyword(s):  
Geometric Proof ◽  
Characteristic 2 ◽  
Quartic Surfaces

Let $k$ be a field of characteristic $2$. We give a geometric proof that there are no smooth quartic surfaces $S\subset \mathbb{P}_{k}^{3}$ with more than 64 lines (predating work of Degtyarev which improves this bound to 60). We also exhibit a smooth quartic containing 60 lines which thus attains the record in characteristic $2$.

scholarly journals Lines on K3 Quartic Surfaces in Characteristic 2

2017 ◽  
Author(s):  
Davide Cesare Veniani
Keyword(s):  
Characteristic 2 ◽  
Quartic Surfaces

A Geometric Proof of Total Positivity for Spline Interpolation.

1984 ◽  
Author(s):  
C. de Boor ◽  
R. DeVore
Keyword(s):  
Spline Interpolation ◽  
Total Positivity ◽  
Geometric Proof

scholarly journals Ulrich bundles on quartic surfaces with Picard number 1

2013 ◽  
Vol 351 (5-6) ◽  
pp. 221-224 ◽  
Author(s):  
Emre Coskun
Keyword(s):  
Picard Number ◽  
Quartic Surfaces

scholarly journals Two algebraic deformations of a K3 surface

1981 ◽  
Vol 82 ◽  
pp. 1-26
Author(s):  
Daniel Comenetz
Keyword(s):  
Hyperelliptic Curve ◽  
Double Cover ◽  
Rational Curves ◽  
K3 Surface ◽  
Quartic Surface ◽  
Quadric Cone ◽  
Birational Model ◽  
Affine Line ◽  
Characteristic 2 ◽  
General Member

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.

scholarly journals Germline Transformation of Drosophila virilis With the Transposable Element mariner

Genetics ◽  
1996 ◽  
Vol 143 (1) ◽  
pp. 365-374 ◽  
Author(s):  
Allan R Lohe ◽  
Daniel L Hartl
Keyword(s):  
Transposable Element ◽  
Common Ancestor ◽  
Pcr Amplification ◽  
Drosophila Virilis ◽  
Cell Region ◽  
Diverse Species ◽  
Drosophila Mauritiana ◽  
Characteristic 2 ◽  
In Situ Hybridizations

Abstract An important goal in molecular genetics has been to identify a transposable element that might serve as an efficient transformation vector in diverse species of insects. The transposable element mariner occurs naturally in a wide variety of insects. Although virtually all mariner elements are nonfunctional, the Mosl element isolated from Drosophila mauritiana is functional. Mosl was injected into the pole-cell region of embryos of D. virilis, which last shared a common ancestor with D. mauritiana 40 million years ago. Mosl PCR fragments were detected in several pools of DNA from progeny of injected animals, and backcross lines were established. Because Go lines were pooled, possibly only one transformation event was actually obtained, yielding a minimum frequency of 4%. Mosl segregated in a Mendelian fashion, demonstrating chromosomal integration. The copy number increased by spontaneous mobilization. In situ hybridization confirmed multiple polymorphic locations of Mosl. Integration results in a characteristic 2-bp TA duplication. One Mosl element integrated into a tandem array of 370-bp repeats. Some copies may have integrated into heterochromatin, as evidenced by their ability to support PCR amplification despite absence of a signal in Southern and in situ hybridizations.

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

scholarly journals On the existence of some specific elements in finite fields of characteristic 2

2012 ◽  
Vol 18 (4) ◽  
pp. 800-813 ◽  
Author(s):  
Peipei Wang ◽  
Xiwang Cao ◽  
Rongquan Feng
Keyword(s):  
Finite Fields ◽  
Characteristic 2

scholarly journals On equations of finite fields of characteristic 2 and APN functions

2015 ◽  
Vol 12 (2-3) ◽  
pp. 75-93
Author(s):  
Nobuo Nakagawa
Keyword(s):  
Finite Fields ◽  
Apn Functions ◽  
Characteristic 2

scholarly journals Elliptic and hyperelliptic curves over supersimple fields in characteristic 2

2006 ◽  
Vol 204 (2) ◽  
pp. 368-379 ◽  
Author(s):  
Amador Martin-Pizarro
Keyword(s):  
Hyperelliptic Curves ◽  
Characteristic 2 ◽  
Elliptic And Hyperelliptic Curves

scholarly journals On the Brauer group of diagonal quartic surfaces

2011 ◽  
Vol 83 (3) ◽  
pp. 659-672 ◽  
Author(s):  
Evis Ieronymou ◽  
Alexei N. Skorobogatov ◽  
Yuri G. Zarhin
Keyword(s):  
Brauer Group ◽  
Quartic Surfaces
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