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

- 2 Want to read
- 10 Currently reading

Published
**1916** by University Press in Cambridge .

Written in English

- Quartic surfaces.

Classifications | |
---|---|

LC Classifications | QA573 J47 |

The Physical Object | |

Pagination | 197p. |

Number of Pages | 197 |

ID Numbers | |

Open Library | OL23328255M |

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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 › Books › Science & Math › Mathematics.

Additional Physical Format: Online version: Jessop, C.M. (Charles Minshall), Quartic surfaces with singular points. Cambridge [Eng.] University Press, Originally published inthis book was written to provide readers with a concise account of the leading properties of quartic surfaces possessing nodes Quartic surfaces with singular points.

book nodal curves. A brief summary of the leading results discussed in the book is included in the form of an introduction. This book will be of value to anyone with an interest in quartic surfaces, algebraic geometry and the history of 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 :// Quartic Surfaces With Singular Points By C.M. Jessop; Old & Rare. Quartic Surfaces With Singular Points by C.M. Jessop. In Stock $ inc. GST. pages.

No dust jacket. This is an ex-Library book. Green cloth with gilt lettering. This is an ex-Library book. Green cloth with gilt lettering. Expected library inserts, stamps and /quartic-surfaces-with-singular-points/MHA.

Quartic Surfaces With Singular Points (Classic Reprint) by darij / main page. Quartic Surfaces With Singular Points (Classic Reprint) 9 Hours Ago The classiﬁcation of ruled quartic surfaces in the book of W.L. Edge [7] is identical with the one of Cremona. all the singular points that occur in the successive blow ups of q.

The. Pl The objective of this book is to present for the first time the complete algorithm for roots of the general quintic equation with enough background information to make the key ideas accessible to non-specialists and even to mathematically oriented readers who are not professional mathematicians.

The book includes an initial introductory chapter on group theory and symmetry, Galois theory and = 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]. ~idolga/ Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): (external link) http 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 :// /does-anyone-know-the-classification-of-fourth-order-surfaces. adshelp[at] The ADS is operated by Quartic surfaces with singular points.

book Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A 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. ~xiao/gallery. In the German mathematician Karl Rohn published a substantial paper on the properties of quartic surfaces with triple points, proving (among many other things) that the maximum number of lines contained in a quartic monoid surface is In this paper we study in details this class of surfaces.

We prove that there exists an open subset A ⊆ P K 1 (K is a characteristic zero field) that From now on I assume that S has only singular points of multiplicity 2. The first step in the proof is to show that rational quartic surfaces with isolated double points are CE to quartic surfaces with non isolated singularities.

Assume that S has isolated singularities. Then the rationality of S forces the presence of an elliptic :// surfaces of degree four and give vario us examples of singular quartics with many lines. Mathematics Subject Classiﬁcation.

Primary: 14J25, 14N25; Secondary: 14N20, 14J70 Table 1. Singular ﬁbres of elliptic pencils on smooth quartic surfaces For the geometry of the quartic, it turns out to be crucial how the line ℓ meets the ﬁbres. Following [15, p. 87] we recall the following deﬁnition: Deﬁnition (Lines of the second kind).

The line ℓ on S is of the second kind 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 the 4th degree (in Slovak Section Quadric Surfaces.

In the previous two sections we’ve looked at lines and planes in three dimensions (or \({\mathbb{R}^3}\)) and while these are used quite heavily at times in a Calculus class there are many other surfaces that are also used fairly regularly and The family of quartic surfaces {X λ} is called Dwork pencil.

It is easy to check that X λ is non-singular if and only if λ 4 ≠ When F = C and λ is transcendental over Q, the Neron-Severi lattice N S (X λ) is of rank 19 and the discriminant group of N S (X λ) is isomorphic to (Z / 8) 2 × (Z / 4). (, ) In particular, we prove that nodal quartic double solids with at most six singular points are irrational, and nodal quartic double solids with at least eleven singular points are rational.

View SINGULAR DEL PEZZO SURFACES WHOSE UNIVERSAL TORSORS ARE HYPERSURFACES ULRICH DERENTHAL Abstract. We classify all generalized del Pezzo surfaces (i.e., minimal desin-gularizations of singular del Pezzo surfaces containing only rational double points) whose universal torsors are open subsets of hypersurfaces in aﬃne :// In the context of K3 mirror symmetry, the Greene–Plesser orbifolding method constructs a family of K3 surfaces, the mirror of quartic hypersurfaces in P 3, starting from a special one-parameter family of K3 varieties known as the quartic Dwork show that certain K3 double covers obtained from the three-parameter family of quartic Kummer surfaces associated with a principally real Kummer surfaces without real points.

The set R of singular points of a complex Kummer surface X carries the natural structure of a four-dimensional F 2-aﬃne space. This structure is induced by that of an F 2-aﬃne space on the corresponding subset of the double covering of X by the torus T (details can be found, for example, in [1], [4 Quartic surfaces with 31 base points and a general triple point Let F be the Fermat-type ideal in C [ x, y, z,w ] generated by x 3 − y 3, y 3 − z 3, z 3 − w :// 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 ://?id=1Bmjde9vhLIC. Chapter 2 is devoted to the study of this space of bitangents at a quartic surface with double points.

As a by-product we obtain a partial classi cation of nodal quartic surfaces (cf. Theorem ). Of course, this result is not at all new. One will nd it, e.g., in Rohn’s paper [R] (though not explicitly).~hadan/ $\begingroup$ No, there are three other types — they are described in detail in Jessop's book Quartic surfaces with singular points, Chap.

VIII (but this goes back to M. Noether). For the first type the surface has a tacnode, the two other types are more complicated. $\endgroup$ – abx Dec 29 '18 at 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, Taiwanese Journal of CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): For given B ≥ 1 and ε> 0, we show that the number of rational points on a non-singular cubic surface, not lying on any line, and of height at most B, is Oε(B 46/25+ε) whenever the surface contains a rational line.

Furthermore we show how the technique can be applied to the problem of counting non-trivial rational ?doi= The book is devoted to the {\mathfrak {A}}_5\)-invariant quartic surfaces in at all.

Since the quartic surface S is reduced, our \({\mathbb {P}}^3\) can be identified with either, or, or. Let us start with the A general plane section of S is an irreducible plane quartic curve that has singular points, which implies that the degree of In a 'modern' treatment of the classification of ruled quartic surfaces the classical one is corrected and completed.

The string models of Series XIII of some ruled quartic surfaces (manufactured by L. Brill and by M. Schilling) are based on a result of Rohn concerning curves in P1 P1 of bi-degree (2, 2). This is given here a conceptional ://.