Moduli of abelian varieties information

quotient variety. Hain, Richard (2014-03-25). "Lectures on Moduli Spaces of Elliptic Curves". arXiv:0812.1803 [math.AG]. Arapura, Donu. "Abelian Varieties and...

Historically the first abelian varieties to be studied were those defined over the field of complex numbers. Such abelian varieties turn out to be exactly...

dimension. More precisely, Siegel modular varieties are the moduli spaces of principally polarized abelian varieties of a fixed dimension. They are named after...

of Abelian Varieties and its Applications to Number Theory Néron model Birch–Swinnerton–Dyer conjecture Moduli space for abelian varieties Duality of...

Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles. It is the connected component of the identity...

of Calabi-Yau varieties is an important open problem, and only special cases such as moduli spaces of K3 surfaces or Abelian varieties are understood...

an interpretation as the moduli A g {\displaystyle {\mathfrak {A}}_{g}} of principally polarized complex abelian varieties of dimension g {\displaystyle...

{\displaystyle {\mathcal {M}}_{g}} of such curves, and a moduli space of abelian varieties, A g {\displaystyle {\mathcal {A}}_{g}} , of dimension g {\displaystyle...

concept of abelian variety is the higher-dimensional generalization of the elliptic curve. The equations defining abelian varieties are a topic of study...

considering the dimensions of moduli of Abelian varieties, which shows there are far more complex tori than Abelian varieties. For complex manifolds X {\displaystyle...

higher-dimensional abelian varieties, so the concept of dual becomes more interesting in higher dimensions. Let A be an abelian variety over a field k. We...

Deligne–Mumford moduli space of curves Deligne–Mumford stacks Fourier–Deligne transform Deligne cohomology Deligne motive Deligne tensor product of abelian categories...

(algebraic geometry) Moduli of abelian varieties Shimura variety Modular curve Elliptic cohomology Silverman, Joseph H. (2009). The arithmetic of elliptic curves...

morphism, the period mapping, from the moduli space of curves of a fixed genus, to a moduli space of abelian varieties, is injective (on geometric points)...

János, Book on Moduli of Surfaces Kollár, János (1996), Rational curves on algebraic varieties Mumford, David (1970), Abelian Varieties Mumford, David...

published on moduli spaces, with a theory summed up in his book Geometric Invariant Theory, on the equations defining an abelian variety, and on algebraic...

Oslo 1970, Wolters-Noordhoff 1972 with Ke-Zheng Li: Moduli of supersingular abelian varieties, Springer 1998 as editor with Steenbrink and van der Geer:...

There is also the higher-dimensional complex multiplication theory of abelian varieties A having enough endomorphisms in a certain precise sense, roughly...

of moduli of a curve of genus g, unless g is 2. Much more is known about the hyperelliptic locus in the moduli space of curves or abelian varieties,[clarification...

if d ≥ 5. Rational varieties (varieties birational to projective space) have Kodaira dimension − ∞ {\displaystyle -\infty } . Abelian varieties (the compact...

algebraic varieties whose structure does not reduce to curves or abelian varieties, and yet where a substantial understanding is possible. A complex...

classification of complex manifolds and complex algebraic varieties through the minimal model program and the construction of moduli spaces sets the...

Projective Geometry of Elliptic Curves, Asterisque, Band 137, 1986 with Constantin Kahn, Steven Weintraub Moduli spaces of Abelian surfaces: compactification...

their defining equations, are the abelian varieties, which are the projective varieties whose points form an abelian group. The prototypical examples are...