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Inspired by the ideas of the minimal model program, Shepherd-Barron, Kollár, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In this paper, we discuss one of the simplest examples that fits into this framework: the case of pairs $(X, H)$ consisting of a degree two $K 3$ surface $X$ and an ample divisor $H$ . Specifically, we construct and describe explicitly a geometric compactification ${\bar{P}}_{2}$ for the moduli of degree two $K 3$ pairs. This compactification...

The Lefschetz trace formula for algebraic stacks.

Kai A. Behrend (1993)

Inventiones mathematicae

The line bundles on moduli stacks of principal bundles on a curve.

Biswas, Indranil, Hoffmann, Norbert (2010)

Documenta Mathematica

The line bundles on the moduli of parabolic $G$ -bundles over curves and their sections

Yves Laszlo, Christoph Sorger (1997)

Annales scientifiques de l'École Normale Supérieure

The Local Torelli Theorem. I. Complete Intersection.

C. Peters (1975)

Mathematische Annalen

The Moduli of Super-Null-Correlation Bundles on IP3.

Valery Vedernikov (1986)

Mathematische Annalen

The Moduli of Weierstrass Fibriations Over P1 .

Rick Miranda (1981)

Mathematische Annalen

The moduli scheme M (0, 2, 4) over IP3.

G. Trautmann, Rosa María Miró-Roig (1994)

Mathematische Zeitschrift

The Moduli Space of (3,3,3) Trilinear forms.

Kok Onn Ng (1995)

Manuscripta mathematica

The Moduli Space of 3-Folds with K = 0 may Nevertheless be Irreducible.

Miles Reid (1987)

Mathematische Annalen

The moduli space of commutative algebras of finite rank

Bjorn Poonen (2008)

Journal of the European Mathematical Society

The moduli space of rank- $n$ commutative algebras equipped with an ordered basis is an affine scheme $𝔅_{n}$ of finite type over $ℤ$ , with geometrically connected fibers. It is smooth if and only if $n \leq 3$ . It is reducible if $n \geq 8$ (and the converse holds, at least if we remove the fibers above $2$ and $3$ ). The relative dimension of $𝔅_{n}$ is $\frac{2}{27} n^{3} + O (n^{8 / 3})$ . The subscheme parameterizing étale algebras is isomorphic to ${GL}_{n} / S_{n}$ , which is of dimension only $n^{2}$ . For $n \geq 8$ , there exist algebras that are not limits of étale algebras. The dimension calculations...

The Moduli spaces of Rank 2 Stable Vector Bundles over Veronesean surfaces.

Rosa M. Miro-Roig (1993)

Manuscripta mathematica

The period map for hypersurface sections of high degree of an arbitrary variety

Mark L. Green (1985)

Compositio Mathematica

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