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4 edition of Quartic surfaces with singular points found in the catalog.

Quartic surfaces with singular points

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Published by University Press in Cambridge [Eng.] .
Written in English

    Subjects:
  • Quartic surfaces.

  • Edition Notes

    Statementby C. M. Jessop
    The Physical Object
    Paginationxxxv, 197, [1] p.
    Number of Pages197
    ID Numbers
    Open LibraryOL24153466M
    OCLC/WorldCa64074161

    The universal Kummer threefold is a 9-dimensional variety that represents the total there is a unique quartic hypersurface, called the Coble quartic, whose singular locus is the Kummer variety. We are interested in the moduli space of Coble quartics. must be a singular point on the Kummer surface. The surface and its 16 nodes are. Quartic surfaces with singular points 4/ 5 A treatise on the line complex 3 / 5 The elements of applied mathematics including kinetics, statics, and hydrostatics / /5(2).


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Quartic surfaces with singular points by C. M. Jessop Download PDF EPUB FB2

Excerpt from Quartic Surfaces: With Singular Points A surface which would naturally take a prominent position in such a book is the Kummer surface, together with its special forms, the tetrahedroid and the wave surface, but the admirable work written by the late R.

Hudson, entitled Kummer's Quartic Surface, renders unnecessary the inclusion of this by: Quartic surfaces with singular points. Cambridge [Eng.] University Press, (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: C M Jessop.

Free 2-day shipping. Buy Quartic Surfaces with Singular Points at   Quartic surfaces with singular points by Jessop, C. (Charles Minshall), Publication date Topics Quartic surfaces Publisher Cambridge [Eng.] University Press HTTP" link in the "View the book" box to the left to find XML files that contain more metadata about the original images and the derived formats (OCR results, PDF etcPages: Books to Borrow.

Top American Libraries Canadian Libraries Universal Library Community Texts Project Gutenberg Biodiversity Heritage Library Children's Library. Open Library. Full text of "Quartic surfaces with singular points" See other formats.

The theory of surfaces has reached a certain stage of completeness and major efforts concentrate on solving concrete questions rather than further developing the formal theory. Many of these questions are touched on in this classic volume: such as the classification of quartic surfaces, the description of moduli spaces for abelian surfaces, and the automorphism group of a Kummer surface.

Regarding singular quartic surfaces in $\mathbb C \mathbb{P}^3$, the classical reference is Jessop's book Quartic surfaces with singular points (). An electronic copy of the book is freely available for legal download here. CLASSIFICATION OF NORMAL QUARTIC SURFACES WITH IRRATIONAL SINGULARITIES YUJIISHIIANDNOBORUNAKAYAMA Abstract.

If a normal quartic surface admits a singular point thatisnotarationaldoublepoint,thenthesurfaceisdetermined bythetriplet the resent progress of the classification problem of quartic surfaces. Quadric Surfaces Example: For the elliptic paraboloid z = 4x2 + y2: xy trace - set z = 0 →0 = 4x2 + y2 This is point (0,0) yz trace - set x = 0 →z = y2 Parabola in yz plane.

xz trace - set y = 0 →y = 4x2 Parabola in xz plane. Trace z = 4 parallel to xy plane: Set z = 4 →4 = 4x2 + y2 or x2 + y2 /4 =1. This is an ellipse parallel to the File Size: 1MB.

Audio Books & Poetry Community Audio Computers, Technology and Science Music, Arts & Culture News & Public Affairs Non-English Audio Spirituality & Religion. Librivox Free Audiobook. Full text of "Quartic surfaces with singular points" See other formats. = 2C2= are singular points of X. The Abel-Jacobi map C!Jac(C);x7!(R x x 0.

1; R x x 0. 2) mod embeds Cinto Jac(C) and the images of the curves C+ are the 16 trope-conics of X. Ernst Kummer In Ernst Kummer had shown that the Fresnel’s wave surface represents a special case of a 3-parametrical family of nodal quartic surfaces [21].

Books to Borrow. Top American Libraries Canadian Libraries Universal Library Community Texts Project Gutenberg Biodiversity Heritage Library Children's Library. Open Library. Books by Language Additional Collections. Featured Full text of "Quartic surfaces with singular points".

order qty: Originally published inthis book was written to provide readers with a concise account of the leading properties of quartic surfaces possessing nodes or nodal curves.

A brief summary of the leading results discussed in the book is included in the form of an introduction. complex K3 quartic surface with 52 lines and 2 singular points of type A1, whose equation is not known.

Non-K3 complex quartic surfaces have been studied by González Alonso and Rams [7]. If they are not ruled by lines, they can contain at most 48 lines. They also conjecture that the actual bound is Singular points of real quartic and quintic curves David A. Weinberg1, Nicholas J. Willis2•* 1 Department of Mathematics and Statistics, Texas 'T'ech University Lubbock, TXStates of America 2 Department of Mathematics Computer Science and Engineering, George Fox Uni­ versity, Newberg, ORUnited States of America.

On the computation of singular plane curves and quartic surfaces In this section we compute equa tions of singular quartic surfaces Enumeration of combinations of rational double points Author: Carlos Rito.

The classification of singular points of real quartic curves is originally due to D.A. Gudkov [2,3,4,5]. He determined the individual types of singular points, as well as all possible sets of singular points that real quartic curves can have. In this paper, we will derive the thirteen individual types of singular points for.

On Surfaces of Maximal Sectional Regularity Brodmann, Markus, Lee, Wanseok, Park, Euisung, and Schenzel, Peter, Taiwanese Journal of Mathematics, ; Galois points on quartic surfaces YOSHIHARA, Hisao, Journal of the Mathematical Society of Japan, ; Isomorphic Quartic K3 Surfaces in the View of Cremona and Projective Transformations Oguiso, Keiji, Cited by: 9.

On the other hand, a projective quartic surface is a surface in projective space P 3 of the same form, but now f is a homogeneous polynomial of 4 variables of degree 4, so for example f(x,y,z,w) = x 4 + y 4 + xyzw + z 2 w 2 − w 4.

Ruled quartic surfaces, models and classification The classification of ruled quartic surfaces in the book of W.L. Edge [7] is identical with the one of Cremona. this singular point. Construction. For any quadric line complex, the lines of the complex in a plane envelop a quadric in the plane.

A Plücker surface depends on the choice of a quadric line complex and a line, and consists of points of the quadrics associated to the planes through the chosen line.

The paper [5] contains a complete classification of smooth complex quartic surfaces with many lines. Finally, lines on complex quartics with singular points are considered in [20], [8].

The Fermat surface 4,6, 8, 12,20 this is the best known example of a surface. Lines on quartic surfaces. singular spatial quartic surface is 64 (respectively, 56). At this point it is appropriate to call attention to the difference betw een the. Segre, B.: The maximum number of lines lying on a quartic surface.

Oxf. Quart. 14(1), () Tereňová, Z.: Lines and singular points on algebraic surfaces of. Quartic surfaces. A deformation of quartics. We arrive at singular surfaces at an intermediate stage as well as at the end. Equation: (x^)^2+(y^)^2+(z^)^2=s, for s going from to 2.

Riemann surface in cover over the plane, with two ramification points. Algebraic quartic surfaces are a classical subject of algebraic geometry and the study of their rich properties has been developed in research papers and books since the XIX century.

Many di erent classi cations for several classes of quartic surfaces where introduced (for instance, see [11], the books [6] and [4];Author: Mauro Carlo Beltrametti, Alessandro Logar, Maria Laura Torrente. We compute the Jacobian of these equations and derive the algebraic equation of the surface of points in C + (P 2) for which this Jacobian is singular, called the singularity surface of the manipulator.

For the general planar platform manipulator this surface is a quartic surface Cited by: In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).It is a hypersurface (of dimension D) in a (D + 1)-dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables (D = 1 in the case of conic sections).

This results in 16 singularities, at the 2-torsion points of A. The minimal resolution of this quotient is a genus 3 K3 surface. A non-singular degree 4 surface in P3 is a genus 3 K3 surface. The intersection of a quadric and a cubic in P4 gives genus 4 K3 surfaces. A quartic surface without singular curves may have at most 16 singular points.

Fact Let V be a normal quartic surface. a) Then, not more than three singular points on V may be collinear. b) If three singular points on V are collinear then the line connecting them lies on V. Proof. b) Otherwise, this line would meet V in each of the three File Size: KB.

Given a quartic surface possessing a singular conic and four noncoplanar isolated singular points, previously known to bear two families of conic curves, (i) along any conic from either family the surface is tangent to a quadric cone whose vertex lies on a line through one of the pairs of singular points, and (ii) the families of conics Cited by: SINGULAR KUMMER SURFACES AND HILBERT MODULAR FORMS* by H.

ResnilcofS For my brother Kumrner surface is a quartic surface in P, which has the maximum ibIe number of point singularities, namely, sixteen. The first exampIe surface of this type was published in by the physicist Fresne1 [I This work discovers the equivalence relation between quadrilateral meshes and meromorphic quartic differentials.

Each quad-mesh induces a conformal structure of the surface, and a meromorphic quartic differential, where the configuration of singular vertices corresponds to the configurations of the poles and zeros (divisor) of the meromorphic differential.

J.-G. Yang, Enumeration of combinations of rational double points on quartic surfaces, in Singularities and complex geometry (Beijing, ), AMS/IP Studies in Advanced Mathematics, Vol.

5 (American Mathematical Society, Providence, RI, ), pp. –, MR Google ScholarAuthor: Çi̇sem Güneş Aktaş. We test the methods for computing the Picard group of a K3 surface in a situation of high rank. The examples chosen are resolutions of quartics in P 3 having 14 singularities of type A 1.

Our computations show that the method of R. van Luijk works well when sufficiently large primes are by: 2. The Kummer involution has 16 fixed points: the 16 2-torsion point of the Jacobian, and they are the 16 singular points of the quartic surface. Resolving the 16 double points of the quotient of a (possibly nonalgebraic) torus by the Kummer involution gives a K3 surface with 16 disjoint rational curves; these K3 surfaces are also sometimes called Kummer surfaces.

The Geometry of Smooth Quartics Jakub Witaszek Born 1st December in Pu lawy, Poland June 6, The set of singular points of a variety X. Pic(X) The Picard group of a scheme X. Pic The set of Gauss swallowtail points on a surface S. q The polar locus of a point. Both 1 and 2 follow by analysing the configuration of lines lying on each element of F AE and F AB.

Our main motivation is to study the singular H 2,2 quartic surfaces arising in the study of the moduli space of abelian surfaces of type (1,3)Cited by: 4.

Abstract. Motivated by our study (elsewhere) of linear syzygies of homogenous ideals generated by quadrics and their intersections to subvarieties of the ambient projective space, we investigate in this note possible zero-dimensional intersections of two Veronese surfaces in P The case of two Veronese surfaces in P 5 meeting in 10 simple points appears also in work of Coble, Cited by: 5.

An algebraic surface of surface order 4. Unlike cubic surfaces, quartic surfaces have not been fully classified. Examples of quartic surfaces include the apple surface, Bohemian dome, Cassini surface, Cayley cubic Hessian, crossed trough, cushion surface, double sphere, eight surface, elliptic torus, Goursat's surface, lemon surface, Menn's surface, miter surface, Nordstrand's weird surface.

IBB Abelian varieties and Related Topics in Algebraic Geometry Since I do not feel qualified nor well-informed, I entirely omitted to list, let alone to comment on, the extensive literature on abelian varieties and Siegel domains from the point of view of Author: Tadao Oda.In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.

Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function of a square .Ruled quartic surfaces, models and classification using the singular locus 22 does not occur as singular locus Lemma The singular locus of a quartic ruled surface cannot be a conic.

Proof Suppose that the conic D, lying in a plane H P(V), is the singular locus of some ruled quartic surface S, corresponding to a curve C P(2V Cited by: 7.