Download 16, 6 Configurations and Geometry of Kummer Surfaces in P3 by Maria R. Gonzalez-Dorrego PDF

By Maria R. Gonzalez-Dorrego

This monograph reviews the geometry of a Kummer floor in ${\mathbb P}^3_k$ and of its minimum desingularization, that is a K3 floor (here $k$ is an algebraically closed box of attribute diversified from 2). This Kummer floor is a quartic floor with 16 nodes as its merely singularities. those nodes supply upward thrust to a configuration of 16 issues and 16 planes in ${\mathbb P}^3$ such that every aircraft includes precisely six issues and every aspect belongs to precisely six planes (this is named a '(16,6) configuration').A Kummer floor is uniquely made up our minds through its set of nodes. Gonzalez-Dorrego classifies (16,6) configurations and stories their manifold symmetries and the underlying questions about finite subgroups of $PGL_4(k)$. She makes use of this data to provide an entire type of Kummer surfaces with particular equations and particular descriptions in their singularities. furthermore, the gorgeous connections to the idea of K3 surfaces and abelian forms are studied.

Show description

Read Online or Download 16, 6 Configurations and Geometry of Kummer Surfaces in P3 PDF

Similar algebraic geometry books

Algebraic geometry: an introduction to birational geometry of algebraic varieties

The purpose of this ebook is to introduce the reader to the geometric concept of algebraic kinds, specifically to the birational geometry of algebraic kinds. This quantity grew out of the author's e-book in eastern released in three volumes by way of Iwanami, Tokyo, in 1977. whereas penning this English model, the writer has attempted to arrange and rewrite the unique fabric in order that even newcomers can learn it simply with out touching on different books, comparable to textbooks on commutative algebra.

Sheaves in Topology

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a unique area into delicate manifolds, a good geometrical suggestion because of R. Thom and H. Whitney. those sheaves, generalizing the neighborhood platforms which are so ubiquitous in arithmetic, have strong purposes to the topology of such singular areas (mainly algebraic and analytic complicated varieties).

Undergraduate algebraic geometry

Algebraic geometry is, basically, the examine of the answer of equations and occupies a crucial place in natural arithmetic. With the minimal of must haves, Dr. Reid introduces the reader to the elemental options of algebraic geometry, together with: airplane conics, cubics and the gang legislation, affine and projective forms, and nonsingularity and measurement.

Vector Bundles on Complex Projective Spaces

Those lecture notes are meant as an creation to the tools of class of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as attainable now we have regularly limited ourselves to the case X = Fn. in response to Serre (GAGA) the class of holomorphic vector bundles is similar to the type of algebraic vector bundles.

Additional resources for 16, 6 Configurations and Geometry of Kummer Surfaces in P3

Sample text

Then VjA = Wfcj fl Wk2 H wjfe8, where 1 < ^1,^2,^3 < 6 and p £ {ki, &2, ^3}. Since the planes wj, 1 < j < 6 are in general position, VjA £ wp, as desired. Case 2. No three of the Vjt, 1 < / < 4, are contained in a plane wp with 1 < p < 6. Associated with each Vjt we have a three element set Mi = {ku, &2i, k$i} C { 1 , . . 2) p | MI = 0. 2), U J = 1 M j = { 1 , . . , 6 } . 4) #(M1nM3) = #(M2nM4) = l #(Mj n Mi) = # ( M 2 n M») = o. 4. (16,6) CONFIGURATIONS AND GEOMETRY OF KUMMER SURFACES IN P 3 .

43. I V . A n o n - d e g e n e r a t e (16,6) configuration in P 3 is of t h e form (a, b, c, d) of ( 1 . 4 . 1 ) . 44. We say that a set of planes is in general linear p o s i t i on if no four of them pass through the same point. 45. 6, up to an automorphism of P 3 . in P 3 is of the form de- Proof. 1). As usual, let us denote a plane in P 3 by a 4-tuple of elements of k. We may view this 4-tuple as a point in P 3 . Let V denote the open subset of (P 3 ) 6 consisting of all the ordered 6-tuples of planes in general linear position.

59. For a subset M of the entries of the 4 x 4 diagram, let the s p an of M be the set of all rows and all columns of the matrix which contain at least one element of M. It is easy to see from definitions that a four element subset M of {vj}i

Download PDF sample

Rated 4.78 of 5 – based on 19 votes