By Maria R. Gonzalez-Dorrego

ISBN-10: 0821825747

ISBN-13: 9780821825747

This monograph stories 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 provide upward thrust to a configuration of 16 issues and 16 planes in ${\mathbb P}^3$ such that every airplane comprises precisely six issues and every element belongs to precisely six planes (this is named a '(16,6) configuration').A Kummer floor is uniquely decided via its set of nodes. Gonzalez-Dorrego classifies (16,6) configurations and reports their manifold symmetries and the underlying questions on finite subgroups of $PGL_4(k)$. She makes use of this data to offer a whole type of Kummer surfaces with particular equations and specific descriptions in their singularities. additionally, the attractive connections to the idea of K3 surfaces and abelian kinds are studied.

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

**Similar algebraic geometry books**

**Iterated Integrals and Cycles on Algebra by Bruno Harris PDF**

This topic has been of significant curiosity either to topologists and to quantity theorists. the 1st a part of this e-book describes many of the paintings of Kuo-Tsai Chen on iterated integrals and the elemental team of a manifold. the writer makes an attempt to make his exposition available to starting graduate scholars.

**George E. Andrews, Bruce C. Berndt's Ramanujan's Lost Notebook: Part IV PDF**

In the spring of 1976, George Andrews of Pennsylvania kingdom collage visited the library at Trinity university, Cambridge, to check the papers of the past due G. N. Watson. between those papers, Andrews chanced on a sheaf of 138 pages within the handwriting of Srinivasa Ramanujan. This manuscript used to be quickly exact, "Ramanujan's misplaced laptop.

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

**Example text**

1), these four points will be coplanar if and only if (a2 — d2)(b2 — c 2 ) — 0. 1). 1) (l f ) abed / 0 , and 9 7 9 7 (2') all of the ± a 2 , ± 6 2 , ± c 2 , ±d2 |N are distinct. 1) have the rank p(S) of Neron-Severi group equal to 2 (for a generic Kummer surface, p(S) = 1) [7]. 1) corresponds to the locus of bielliptic curves in M2 [7]. 57. Consider four points {vjt}i*
*

3) implies that Ta = aT for any a £ Fo. In other words, T belongs to the centralizer of F0 in PGL±(k). 50. Fo is its own centralizer in PGL^{k). Proof. Pick and fix once and for all an element i of k such that i2 + 1 = 0. We have the 4-1 covering 7T : SL4(k) - • PGL4(k), whose kernel is { 1 , - 1 , i , — i } (here we identify constant multiples of the identity matrix with elements of fc). 1) e3 0 0 1 0 0 -1 0 0 <0 1 0 0 0 ( 0 0 0 \^0 0 1 0 0 -1 0 0 0 0 0 0 e2 -1 0 f°0 00 01 and e4 = 0 1 0 \1 0 0 1—1 ei = 1 0 0 0 0 o -1/ 0 j 1 0/ 0\ 0 0 \) 1 0 0 0 (16,6) CONFIGURATIONS AND GEOMETRY OF KUMMER SURFACES IN P 3 .

3). 3), respectively:

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

by Charles

4.5