Get Abelian Varieties: Proceedings of the International PDF

By Herbert Lange, Wolfgang Barth, Klaus Hulek

ISBN-10: 3110144115

ISBN-13: 9783110144116

Booklet by way of Barth, Wolf, Hulek, Klaus

Show description

Read Online or Download Abelian Varieties: Proceedings of the International Conference Held in Egloffstein, Germany, October 3-8, 1993 PDF

Best algebraic geometry books

Download PDF by Andreas L. Knutsen, Trygve Johnsen: K3 Projective Models in Scrolls

The exposition stories projective versions of K3 surfaces whose hyperplane sections are non-Clifford basic curves. those types are contained in rational common scrolls. The exposition vitamins ordinary descriptions of versions of normal K3 surfaces in projective areas of low size, and ends up in a type of K3 surfaces in projective areas of size at so much 10.

Read e-book online Koszul cohomology and algebraic geometry PDF

The systematic use of Koszul cohomology computations in algebraic geometry might be traced again to the foundational paintings of Mark eco-friendly within the Eighties. eco-friendly hooked up classical effects in regards to the excellent of a projective type with vanishing theorems for Koszul cohomology. eco-friendly and Lazarsfeld additionally said conjectures that relate the Koszul cohomology of algebraic curves with the lifestyles of precise divisors at the curve.

Download PDF by Rolf-Peter Holzapfel: The Ball and Some Hilbert Problems

As a fascinating item of mathematics, algebraic and analytic geometry the complicated ball used to be born in a paper of the French Mathematician E. PICARD in 1883. In fresh advancements the ball unearths nice curiosity back within the framework of SHIMURA types but in addition within the concept of diophantine equations (asymptotic FERMAT challenge, see ch.

Additional info for Abelian Varieties: Proceedings of the International Conference Held in Egloffstein, Germany, October 3-8, 1993

Sample text

4] • N o t a t i o n . The following three matrices are elements of finite order in Γι ιΤΙ : / Ο R := 0 1 0 \ 0 1 0 0 - 1 0 - 1 0 \ 0 0 0 1 J equal to Ueno III(2)a = J 0 (X 4 , H2) S := f 0 0 -1 0 \ 0 1 0 0 1 0 1 0 \ 0 0 0 1 ) equal to Ueno III(4)a = / 0 (X, 1 2 ) Τ / 0 0 -1 0 1 0 1 0 0 \ 0 0 0 equal to Ueno III(5)a = I 0 (Y, H2). := 0 \ 0 0 1 ) We determine the relations T 2 = S3 = Iq , S 4 = R. Their fixed varieties are given as follows ( ρ := exp (^f 1 )): C\ = {ρ} χ Η is fixed by R,S C2 = {i} x Η is fixed by T.

Every involution in ΓιιΤΙ is conjugate with respect to Γι >η to exactly one of the following matrices in dependence on η mod 4. 1) η ξ ± 1 mod 4 ; /ο,^3· 2) η Ξ 0 mod 4 : Ιο,Ιχ,Ι^,Ι^. 3) η = 2 mod 4 : J 0 , Ji, J2, J3, J4· Proof. Every involution in Γι )ΤΙ is conjugate to Jo or J3 in Sp(4, Z ) by the Uenoclassification. Therefore it suffices to investigate how the conjugacy classes of I0J3 split in Γι ι Τ Ι . 3 we get the involutions Jo, (Ji), (J2) in dependence on n. 3. • 3. The case η > 4 Throughout the following sections we collect elements of Γ ι ) η having a fixed point Ζ G KI2 with isotropy group I s o Z = { j e Γ ι ι η | g • Ζ = Ζ } ; it is clear how to generalize this concept to an arbitrary submanifold of H2 .

35 Branch points in moduli spaces of certain abelian surfaces vi P r o o f . L e t ω υ2 be a fixed point of I3 with gcd (ui, "3 υ4 J c, d , A , B , which satisfy the properties: — mine integers a, b, t>i3 : = gcd(t;i,ü3) = αν ι + bv 3, gcd v24 ( ν 2 , ν 4 ) = c v v + 2 4, dv = V3,V4) , 2 A v 13 + 1. Deter- B v 2 1. = 4 The equation for the fixed point ω of I3 yields the existence of an integer Λ with Λυχ = — υι — V2 mod η λν 2 = v 2 mod η = — U3 mod η Xvs Aui = — vz v^ mod n . Combining the above congruences we get in particular a v 13 (A + 1) mod —ν = 2 η , - dv3 (1 — λ ) mod n.

Download PDF sample

Abelian Varieties: Proceedings of the International Conference Held in Egloffstein, Germany, October 3-8, 1993 by Herbert Lange, Wolfgang Barth, Klaus Hulek


by James
4.2

Rated 4.74 of 5 – based on 10 votes