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A new family of rational surfaces in P4

Hans-Christian Graf v. Bothmer, Cord Erdenberger, Katharina Ludwig
2005 Journal of symbolic computation  
We describe a new method of constructing rational surfaces with given invariants in P^4 and present a family of degree 11 rational surfaces of sectional genus 11 with 2 six-secants that we found with this  ...  In this paper we describe a new method for finding rational surfaces in P 4 and present a new family of rational degree 11 surfaces in P 4 which we found with this method.  ...  Recently Abo announced the existence of a family of degree 12 rational surfaces in P 4 .  ... 
doi:10.1016/j.jsc.2004.09.003 fatcat:qlac4atgdrfrlozrcoetc77w3y

Page 2955 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
The characteristic polynomial P4(x) of ® acting on the Tate module T;(A), for any / # p, is a monic polynomial of degree 2g with coefficients in the ring of integers Z.  ...  A family of Mumford type is a one-dimensional family of polar- ized abelian fourfolds as defined by D. Mumford [Math. Ann. 181 (1969), 345-351; MR 40 #1400].  ... 

On surfaces in P6 with no trisecant lines

Sandra Rocco, Kristian Ranestad
2000 Arkiv för matematik  
These surfaces may also be constructed by linkage. Consider a rational surface Blr(P 2) embedded in p5 by the line bundle 41-2E-~6_1 Ei.  ...  A nontrigonal K3-surface of degree 10 in p6 is a linear section of the Plficker embedding of the Grassmannian Gr(2, 5) intersected with a quadric hypersurface.  ...  .~, where S is a smooth surface of degree 8 in p6. Example 1.14. (A family of surfaces of degree 10.)  ... 
doi:10.1007/bf02384319 fatcat:nyfhyqxrejdsnd7ztszxytbkgm

Approximate parameterization by planar rational curves

Bert J�ttler, Pavel Chalmoviansk�
2004 Proceedings of the 20th spring conference on Computer graphics - SCCG '04  
After briefly discussing exact methods for parameterization and methods for rational interpolation, we describe a new technique for rational parameterization.  ...  In addition, we use a region-growing-type approach in order to obtain a good initial solution, which is crucial for the convergence of the nonlinear optimization procedure.  ...  Acknowledgements The research of the first author was partly supported by the Fifth Framework Programme of the EU via project GAIA II (IST 2001-35512) entitled "Intersection algorithms for geometry based  ... 
doi:10.1145/1037210.1037215 dblp:conf/sccg/JuttlerC04 fatcat:xg2t2kdo7ffcfe577nog5wgesy

Page 2314 of Mathematical Reviews Vol. , Issue 85f [page]

1985 Mathematical Reviews  
In a recent paper the author [same journal 187 (1984), no. 2, 209-219] gave a description of all smooth surfaces of degree 7 in P4.  ...  Precisely, we prove that if on the semistable family a: X — A of surfaces of general type the relative canonical divisor re ee ee -C>0 for all complete curves C contained in X (so that in particular the  ... 

Zero cycles on del Pezzo surfaces over local fields

Kevin R Coombes, Douglas J Muder
1985 Journal of Algebra  
Firstly, their intersection point is a rational point on X. Next, there is a one-dimensional family of hyperplanes in P4 containing Y.  ...  We first construct a good family of de1 Pezzo surfaces of degree 4 (written V") with all rational lines.  ...  If u(a) = u(b)= o(b -a), then v(Q) < = ~(4) + u(a) = v(d) + u(b). Since o(b) is even, this forces ~(4) to be even and A,(X)=O.  ... 
doi:10.1016/0021-8693(85)90057-2 fatcat:dvy3cftivfaonb6sylcpfdzqyy

Page 484 of Mathematical Reviews Vol. , Issue 85b [page]

1985 Mathematical Reviews  
The family of surfaces obtained in this way depends on 6 parameters. Recall that a general Enriques surface depends on 10 parameters.  ...  The Reye congruences form an irreducible 9- dimensional family in the (10-dimensional) moduli space of En- riques surfaces. The purpose of the paper is to characterize this family geometrically.  ... 

Birkhoff strata of Sato Grassmannian and algebraic curves [article]

B.G. Konopelchenko, G. Ortenzi
2013 arXiv   pre-print
For the big cell the subbundle TB_W_∅ represents the tower of families of normal rational (Veronese) curves of all degrees.  ...  Two methods of regularization of singular curves contained in TB_W_Ŝ, namely, the standard blowing-up and transition to higher strata with the change of genus are discussed.  ...  This work has been partially supported by PRIN grant no 28002K9KXZ and by FAR 2009 (Sistemi dinamici Integrabili e Interazioni fra campi e particelle) of the University of Milano Bicocca .  ... 
arXiv:1005.2053v3 fatcat:mfp4oteuobhxfo5c6n3c5usk6m

Insights Into the Role of Exposed Surface Charged Residues in the Alkali-Tolerance of GH11 Xylanase

Xiuyun Wu, Qun Zhang, Lanzeng Zhang, Shijia Liu, Guanjun Chen, Huaiqiang Zhang, Lushan Wang
2020 Frontiers in Microbiology  
In this study, a rational structure-based design was conducted based on a thermostable GH11 xylanase TlXynA from Thermomyces lanuginosus to improved pH-tolerance.  ...  Four mutant enzymes (P1, P2, P3, and P4) and five variants (N1, N2, N3, N4, and N5) were constructed by substituting surface charged residue combinations using site-directed mutagenesis.  ...  This method to rationally design charged surface residues has paved a new way for understanding and engineering acid and alkali stable xylanases and for characterizing other enzymes.  ... 
doi:10.3389/fmicb.2020.00872 pmid:32457729 pmcid:PMC7225583 fatcat:h26w2aglh5dpnbmwgz263yn4aq

Notes on the arithmetic of Fano threefolds [chapter]

YU. I. MANIN
1996 World Scientific Series in 20th Century Mathematics  
Jacobian of V4 ( [New] , [Rel] ).  ...  Actually, for d=4 general W4 are smooth quartics in P4, ((4; 4) in notation of 1. la), but they admit flat specialization W4, which can be realized as a double cover of a quadric Q3 ~ p4 ramified along  ... 
doi:10.1142/9789812830517_0020 fatcat:fbyoggqqvnc6tgz4asmknbuisa

Page 1428 of Mathematical Reviews Vol. , Issue 90C [page]

1990 Mathematical Reviews  
“As a new result we present a detailed calculation of the volume of the lattice spanned by K-integral vectors tangent to a K-rational point of # with respect to the Polyakov measure using a Riemann- Roch  ...  The authors describe a family of rational plane sextic curves S, (each of which in general has ten nodes) admitting six tritangents and parametrized by x € P®, the complex projective 3-space.  ... 

Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties

Victor V. Batyrev, Duco van Straten
1995 Communications in Mathematical Physics  
First, Φ_0 is defined by intersection numbers of rational curves in P_Σ with the hypersurfaces V_i and their toric degenerations.  ...  We formulate general conjectures about the relationship between the A-model connection on the cohomology of a d-dimensional Calabi-Yau complete intersection V of r hypersurfaces V_1, ..., V_r in a toric  ...  Morrison whose numerous remarks concerning a preliminary version of the paper helped us to give precise references on his work, especially on the forthcoming papers [18, 35] .  ... 
doi:10.1007/bf02101841 fatcat:a2klhlbjsjcanovxqhrdr4nhqe

Connection formulae for degenerated asymptotic solutions of the fourth Painleve equation [article]

Andrei A. Kapaev (St.Petersburg Department of Steklov Mathematical Institute)
1998 arXiv   pre-print
All possible 1-parametric classical and transcendent degenerated solutions of the fourth Painleve equation with the corresponding connection formulae of the asymptotic parameters are described.  ...  Painlevé functions [26] . 2) Other family of rational solutions described in ref  ...  In fact, these special cases correspond to the rational solutions of the equation P4 described above.  ... 
arXiv:solv-int/9805011v1 fatcat:j6mnozxybfh5jjrla33y26mq34

In search of non-conventional surface oxidic motifs of Cu on Au(111)

Taehun Lee, Yonghyuk Lee, Kisung Kang, Aloysius Soon
2016 Physical Chemistry, Chemical Physics - PCCP  
of new non-conventional, non-hexagonal surface oxidic structures in this system.  ...  Using first-principles density-functional theory calculations, we systematically examine and analyze the detailed atomic structure and surface energetics of various oxidic motifs of Cu on Au(111), in search  ...  this work into two families of surface oxides, namely the p2-motifs and the p4-motifs.  ... 
doi:10.1039/c5cp07932b pmid:26899930 fatcat:qq4st4h4enhsfnbmhjtkkilcaa

On the Noether-Lefschetz theorem and some remarks on codimension-two cycles

Phillip Griffiths, Joe Harris
1985 Mathematische Annalen  
than complete intersections of X with a surface S C p4.  ...  Let }X~I be a general pencil with base locus B = Xo-Xoo a smooth surface of degree d 2 in p4.  ... 
doi:10.1007/bf01455794 fatcat:mvlvf57e7ngyrmtcn7wfz4iyce
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