Download Free Compactification Of Siegel Moduli Schemes Book in PDF and EPUB Free Download. You can read online Compactification Of Siegel Moduli Schemes and write the review.

The main result of this monograph is to prove the existence of the toroidal compactification over Z(1/2).
The Siegel moduli scheme classifies principally polarised abelian varieties and its compactification is an important result in arithmetic algebraic geometry. The main result of this monograph is to prove the existence of the toroidal compactification over Z (1/2). This result should have further applications and is presented here with sufficient background material to make the book suitable for seminar courses in algebraic geometry, algebraic number theory or automorphic forms.
The main result of this monograph is to prove the existence of the toroidal compactification over Z(1/2).
This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.
This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps. Both advanced graduate students and researchers in algebraic geometry will find this book a valuable read.
Abelian varieties and their moduli are a topic of increasing importance in today`s mathematics, applications ranging from algebraic geometry and number theory to mathematical physics. This collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field.
Olsson gives modular compactifications of the moduli of toric pairs and the moduli of polarized abelian varieties A [subscript g,[delta]] in (Ols08). We give alternative constructions of these compactifications by using mirror symmetry. Our constructions are toroidal compactifications. The data needed for a toroidal compactification is a collection of fans. We obtain the collection of fans from the Mori fans of the minimal models of the mirror families. Moreover, we reinterpretate the compactification of A [subscript g,[delta]] in terms of KSBA stable pairs. We find that there is a canonical set of divisors S(K2) associated with each cusp. Near the cusp, a polarized semiabelic scheme (X, G,L) is the canonical degeneration given by the compactification if and only if (X , G, [theta]) is an object in A P[subscript g,d] for any [theta] [element of] S(K2). The two compactifications presented here are a part of a general program of applying mirror symmetry to the compactification problem of the moduli of Calabi-Yau manifolds. This thesis contains the results in (Zhu14b) and (Zhu14a).