Posted in Algebraic Geometry

Read e-book online 16, 6 Configurations and Geometry of Kummer Surfaces in P3 PDF

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 diverse from 2). This Kummer floor is a quartic floor with 16 nodes as its basically singularities. those nodes provide 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 made up our minds by way of 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 offer an entire class of Kummer surfaces with specific equations and specific descriptions in their singularities. moreover, the attractive connections to the speculation of K3 surfaces and abelian kinds are studied.

Show description

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

Best algebraic geometry books

Get Sheaves on manifolds PDF

From the studies: This booklet is dedicated to the learn of sheaves by way of microlocal tools. .(it) may possibly function a reference resource in addition to a textbook in this new topic. Houzel's old evaluation of the improvement of sheaf idea will establish vital landmarks for college kids and should be a excitement to learn for experts.

Download e-book for kindle: Geometric Modular Forms and Elliptic Curves by Haruzo Hida

This e-book presents a finished account of the speculation of moduli areas of elliptic curves (over integer earrings) and its software to modular kinds. the development of Galois representations, which play a basic position in Wiles' evidence of the Shimura-Taniyama conjecture, is given. additionally, the e-book offers an summary of the evidence of numerous modularity result of two-dimensional Galois representations (including that of Wiles), in addition to a few of the author's new ends up in that path.

David Mumford, M. Nori, P. Norman's Tata Lectures on Theta III PDF

The second one in a sequence of 3 volumes surveying the idea of theta services, this quantity supplies emphasis to the designated houses of the theta services linked to compact Riemann surfaces and the way they result in strategies of the Korteweg-de-Vries equations in addition to different non-linear differential equations of mathematical physics.

New PDF release: Current Trends in Arithmetical Algebraic Geometry

Mark Sepanski's Algebra is a readable creation to the pleasant international of recent algebra. starting with concrete examples from the learn of integers and modular mathematics, the textual content gradually familiarizes the reader with better degrees of abstraction because it strikes during the examine of teams, earrings, and fields.

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

Example text

3). 3), respectively:

3) together with det ei = 1 imply that both e$ and e 4 commute with e2. 2), e 4 must commute with both e 2 and e3, hence e 4 must be a diagonal matrix with eigenvalues 1,-1,-1. But then e 4 belongs to the subgroup of SL^k) generated by e 2 and e3, which is a contradiction. The Sublemma is proved. • From now on we assume that e2j = 1, 1 < j < 4. Then each of the e7- is a diagonaHzable matrix with eigenvalues 1,1,-1,-1. 2) imply that for 2 < j < 4, e^ej = ±eje\. Next, we may assume that at least two of the ej, 2 < j < 4, actually commute with e\.

We have a natural action of N on Fo by conjugation. View Fo as a 4-dimensional vector space over F2 on which N acts by linear automorphisms. 1) ^ — GL4(¥2) (note that GL4(¥2) = PGL4(¥2) = SL4(¥2))The point of the next theorem is to show that -p- can be identified with Sp4{¥2) for a suitable symplectic structure on F 0 = F*. Next we describe the symplectic structure on Fo which is preserved by N. Namely, consider any four element subgroup H of Fo. We may think of such a subgroup as a 2-plane in our 4-dimensional vector space F | .

Download PDF sample

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

by Jason

Rated 4.49 of 5 – based on 45 votes