By Maria R. Gonzalez-Dorrego

ISBN-10: 0821825747

ISBN-13: 9780821825747

This monograph reports 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 assorted from 2). This Kummer floor is a quartic floor with 16 nodes as its simply singularities. those nodes supply upward thrust to a configuration of 16 issues and 16 planes in ${\mathbb P}^3$ such that every airplane includes precisely six issues and every aspect belongs to precisely six planes (this is termed a '(16,6) configuration').A Kummer floor is uniquely decided by way of its set of nodes. Gonzalez-Dorrego classifies (16,6) configurations and experiences their manifold symmetries and the underlying questions on finite subgroups of $PGL_4(k)$. She makes use of this data to provide an entire category of Kummer surfaces with particular equations and specific descriptions in their singularities. additionally, the attractive connections to the idea of K3 surfaces and abelian types are studied.

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

**Similar algebraic geometry books**

**New PDF release: Lectures on introduction to moduli problems and orbit spaces**

Backbone name: advent to moduli difficulties and orbit areas.

**Get Higher-Dimensional Algebraic Geometry PDF**

Higher-Dimensional Algebraic Geometry stories the type concept of algebraic kinds. This very energetic sector of analysis continues to be constructing, yet an grand volume of information has collected during the last two decades. The author's objective is to supply an simply obtainable advent to the topic.

**Download PDF by Constance Reid: Hilbert**

Now in new exchange paper variations, those vintage biographies of 2 of the best twentieth Century mathematicians are being published below the Copernicus imprint. those noteworthy money owed of the lives of David Hilbert and Richard Courant are heavily similar: Courant's tale is, in lots of methods, obvious because the sequel to the tale of Hilbert.

That includes a mix of unique learn papers and finished surveys from a global staff of major researchers within the thriving fields of foliation concept, holomorphic foliations, and birational geometry, this e-book provides the complaints of the convention "Foliation idea in Algebraic Geometry," hosted by means of the Simons beginning in big apple urban in September 2013.

- Rigid Analytic Geometry and Its Applications
- Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses
- Grobner bases in commutative algebra
- Hodge Theory and Complex Algebraic Geometry

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

**Sample text**

Then, since 3, 4 and P are not collinear by (c), they span 4', so 4' = P , a contradiction. We have now constructed: V

Similarly, V fl 2 fl 2' = 0. 40. Hence we may assume that V fl 11' = V fl 22' = 0. 35(b)) to find a line in P 3 which meets all the lines of (a) but not V. We take the line 12. The reasoning in case (6) is analogous. The line 3 fl 3 ' meets all the four lines in (a) but not V. • Take a line L satisfying (a)-(c). Let P := L n 3 D 3 ' , R := L fl 4 H 4'. 41. Let us consider a standard (8,4) configuration Let L be a line satisfying (a)-(c). Let P, R be as above. 2). 1). a unique 4', P, R diagram Proof.

Let L be the isotropic line corresponding to (ei,e2), as above, and / the stabilizer of L. By (3) we now know that y- = S4 x F 2 [4, p. [4], line 44]. 2) Fo S4 x F 2 (16,6) CONFIGURATIONS AND GEOMETRY OF KUMMER SURFACES IN P 3 . 2) does not split. 3) 1 -» Fo -> W - ^ 5 3 x F 2 -> 1. does split (for instance, we may send the generator of 1 x F2 to ( - 1 0 0 0 ^ 0 1 0 0 0 0 1 0 0 0 0 1, and the elements of S$ X 1 to permutations on the last three variables). Here and below the identity element in any group will be denoted by 1, even when the group is F2.

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

by Joseph

4.2

- Read e-book online The algebraic theory of modular systems PDF
- Paul Hacking, Radu Laza, Dragos Oprea, Gilberto Bini, Martí's Compactifying Moduli Spaces PDF

Categories: Algebraic Geometry