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The moduli space of cubic fourfolds
We describe the GIT compactification of the moduli space of cubic fourfolds, with a special emphasis on the role played by singularities. Our main result is that a cubic fourfold with only isolatedExpand
The moduli space of cubic fourfolds via the period map
We characterize the image of the period map for cubic fourfolds with at worst simple singularities as the complement of an arrangement of hyperplanes in the period space. It follows then that the GITExpand
Semi-algebraic horizontal subvarieties of Calabi-Yau type
We study horizontal subvarieties $Z$ of a Griffiths period domain $\mathbb D$. If $Z$ is defined by algebraic equations, and if $Z$ is also invariant under a large discrete subgroup in an appropriateExpand
Remarks on degenerations of hyper-K\"ahler manifolds
Using the Minimal Model Program, any degeneration of K-trivial varieties can be arranged to be in a Kulikov type form, i.e. with trivial relative canonical divisor and mild singularities. In theExpand
Maximal Cohen–Macaulay modules over the cone of an elliptic curve
Let R=k[Y1,Y2,Y3]/(f), f=Y13+Y23+Y33, where k is an algebraically closed field with chark≠3. Using Atiyah bundle classification over elliptic curves we describe the matrix factorizations of theExpand
Deformations of singularities and variation of GIT quotients
We study the deformations of the minimally elliptic surface sin- gularity N16. A standard argument reduces the study of the deformations of N16 to the study of the moduli space of pairs (C, L)Expand
The KSBA compactification for the moduli space of degree two K3 pairs
Inspired by the ideas of the minimal model program, Shepherd-Barron, Koll\'ar, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In thisExpand
Recognizing the pitfalls of total quality management
Should utilities be interested in total quality management (TQM) After all, the argument that better quality products should increase the sales and result in higher profits does not readily apply toExpand
The moduli space of cubic threefolds via degenerations of the intermediate Jacobian
Abstract A well known result of Clemens and Griffiths says that a smooth cubic threefold can be recovered from its intermediate Jacobian. In this paper we discuss the possible degenerations of theseExpand
Maximally algebraic potentially irrational cubic fourfolds
A well known conjecture asserts that a cubic fourfold $X$ whose transcendental cohomology $T_X$ can not be realized as the transcendental cohomology of a $K3$ surface is irrational. Since theExpand