The moduli space of cubic threefolds

By Daniel Allcock. 2003

66 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/37a3b87e6971f76651a944ad433651d164d99a38

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Y. Odaka
2. Cristiano Spotti
3. Yuchen Liu
4. Song Sun
5. Chenyang Xu
6. Chi Li
7. R. Laza
8. E. Looijenga

In Geometry and Topology

1. E. Looijenga
2. Cristiano Spotti
3. R. Laza
4. Song Sun
5. Y. Odaka
6. Yuchen Liu
7. Chi Li
8. Daniel Allcock

In Mathematical Physics

1. E. Looijenga
2. R. Laza
3. Song Sun
4. Cristiano Spotti
5. Daniel Allcock
6. J. Carlson
7. Y. Odaka
8. D. Toledo

Citations in the corpus

• The Moduli Space of Cubic Threefolds As a Ball Quotient (2006, methodology): “2 of [2] implies that the threefolds given explicitly in (iii) have closed orbits in PCss; since the orbits miss L, they are also closed in P̂Css.”
• The period map for cubic fourfolds (2007, background): “On the other hand, the summand N0 yields almost the full semi-universal deformation of the simple elliptic singularity p0: we deform in J0 ⊕ J1 ⊕ J2 ⊂ C[t0, t1, t2] and thus get a codimension one subspace transversal to the equisingularity stratum.”
• K-stability of cubic threefolds (2017, background): “icitly yields the proper good quotient moduli space M parametrizing all K-polystable threefolds which can be smoothable to a cubic threefold. K-STABILITY OF CUBIC THREEFOLDS 3 By the classification in [All03], we have a concrete description. Corollary 1.2. We have the following list which gives all t”
• The moduli space of cubic fourfolds (2007, background): “It is also implicitly used in the case of cubic threefolds by Allcock– Carlson–Toledo [4] and Looijenga–Swierstra [18].”
• Complex hyperbolic triangle groups (2003, background): “In summary, there seems to be a critical interval I, such the representations ρt(p, q, r) are discrete embeddings iff t ∈ I. Depending on the endpoints of I, there are either no additional discrete representations, or a countable collection of extra discrete representations.”
• Explicit Gromov-Hausdorff compactifications of moduli spaces of K\"ahler-Einstein Fano manifolds (2017, methodology): “GIT of cubic threefolds is done by Allcock [1].”
• Compact moduli space of Kahler-Einstein Fano varieties (2014, background): “3.2 will be one of the key tools for this direction. For example, the author is tempted to expect that many of the standard GIT moduli spaces of hypersurfaces, such as cubic 3-folds and 4-folds case ([All], [Laza], [Yok1], [Yok2]), are examples of our K-moduli spaces (cf., [OSS, Theorem 3.4 and subs”