Download Compactifying Moduli Spaces for Abelian Varieties by Martin C. Olsson PDF

By Martin C. Olsson

This quantity provides the development of canonical modular compactifications of moduli areas for polarized Abelian forms (possibly with point structure), development at the prior paintings of Alexeev, Nakamura, and Namikawa. this offers a special method of compactifying those areas than the extra classical strategy utilizing toroical embeddings, which aren't canonical. There are major new contributions during this monograph: (1) The creation of logarithmic geometry as understood by way of Fontaine, Illusie, and Kato to the examine of degenerating Abelian types; and (2) the development of canonical compactifications for moduli areas with larger measure polarizations according to stack-theoretic concepts and a examine of the theta group.

Show description

Read or Download Compactifying Moduli Spaces for Abelian Varieties PDF

Best algebraic geometry books

Computer Graphics and Geometric Modelling: Mathematics

Almost certainly the main entire assessment of special effects as obvious within the context of geometric modelling, this quantity paintings covers implementation and idea in a radical and systematic model. special effects and Geometric Modelling: arithmetic, comprises the mathematical heritage wanted for the geometric modeling subject matters in special effects lined within the first quantity.

Infinite Dimensional Lie Groups in Geometry and Representation Theory: Washington, DC, USA 17-21 August 2000

This e-book constitutes the court cases of the 2000 Howard convention on "Infinite Dimensional Lie teams in Geometry and illustration Theory". It provides a few very important fresh advancements during this quarter. It opens with a topological characterization of normal teams, treats between different subject matters the integrability challenge of assorted endless dimensional Lie algebras, offers sizeable contributions to special matters in smooth geometry, and concludes with attention-grabbing functions to illustration concept.

Foundations of free noncommutative function theory

During this ebook the authors improve a concept of unfastened noncommutative features, in either algebraic and analytic settings. Such features are outlined as mappings from sq. matrices of all sizes over a module (in specific, a vector house) to sq. matrices over one other module, which recognize the scale, direct sums, and similarities of matrices.

Additional info for Compactifying Moduli Spaces for Abelian Varieties

Example text

Let f : (X, MX ) → (Y, MY ) be a morphism of fine log schemes locally of finite presentation. For a scheme T and a quasi–coherent sheaf I on T , let T [I] denote the scheme with same underlying topological space as that of T , but with structure sheaf the OT –algebra OT ⊕ I with algebra structure given by (a + i)(c + j) = ac + (aj + ci). The ideal I defines a closed immersion j : T → T [I] for which the natural map T [I] → T induced by OT → OT [I] sending a to a is a retraction. If MT is a fine log structure on T , let MT [I] denote the log structure on T [I] obtained by pullback along OT → OT [I] so that we have a diagram of fine log schemes j π (T, MT ) −−−−→ (T [I], MT [I] ) −−−−→ (T, MT ).

Iv) θ ∈ f∗ L is a section such that for every geometric point s¯ → S the zero locus of the section θs¯ ∈ H 0 (Ps¯, Ls¯) does not contain any T -orbit. 10]) The stack T P fr [Q] is a proper algebraic stack over Z with finite diagonal. 7. 2], a stable semiabelic variety over an algebraically closed field k is a scheme P/k together with an action of a semiabelian scheme G/k such that the following condition holds: 1. The dimension of G is equal to the dimension of each irreducible component of P . 2.

There are only finitely many orbits for the G–action. 4. The stabilizer group scheme of every point of P is connected, reduced, and lies in the toric part T of G. A stable semiabelic pair is a projective stable semiabelic variety P (with action of the semiabelian group scheme G) together with an ample line bundle L on P and a section θ ∈ H 0 (P, L ) whose zero locus does not contain any G–orbits. 8. If S is a scheme, then a stable semiabelic pair over S is a collection of data (G, f : P → S, L , θ ∈ f∗ L ) where: 1.

Download PDF sample

Rated 4.97 of 5 – based on 42 votes