Hodge Representations

Han, Xiayimei; Robles, Colleen

doi:10.1017/exp.2020.55

Cited by 5 publications

(3 citation statements)

References 31 publications

(33 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proof is very similar to the proof of Theorem 5.4 in [Den21], for the definition of the Mumford-Tate group we refer to [GGK13]. By the classification of Hodge representation of type (1, 2, 2, 1) [HRC20], the non-generic Mumford-Tate groups can appear in the following cases (1) A compact maximal torus.…”

Section: Maximal Unipotent Monodromy Point the Precise Mathematical D...mentioning

confidence: 87%

Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

Chen

Güler

Yaylı

et al. 2023

International Electronic Journal of Geometry

View full text Add to dashboard Cite

The theory of finite type submanifolds was introduced by the first author in late 1970s and it has become a useful tool for investigation of submanifolds. Later, the first author and P. Piccinni extended the notion of finite type submanifolds to finite type maps of submanifolds; in particular, to submanifolds with finite type Gauss map. Since then, there have been rapid developments in the theory of finite type. The simplest finite type submanifolds and submanifolds with finite type Gauss maps are those which are of 1-type. The classes of such submanifolds constitute very special and interesting families in the finite type theory.

show abstract

Section: Maximal Unipotent Monodromy Point the Precise Mathematical D...mentioning

confidence: 87%

Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

Chen

Güler

Yaylı

et al. 2023

International Electronic Journal of Geometry

View full text Add to dashboard Cite

show abstract

“…IV.A.2], Any (real) MT-group must contain a compact maximal torus. According to Han and Robles' classification of type (1, 2, 2, 1) Hodge representations in [HR20], all connected reductive subgroups M ≤ Sp(6, Q) that could be a MT-group for some elements in D are (or are contained in):…”

Section: Analysis Of Casementioning

confidence: 99%

Extension of Period Maps by Polyhedral Fans

Deng¹

2021

Preprint

View full text Add to dashboard Cite

Kato and Usui developed a theory of partial compactifications for quotients of period domains D by arithmetic groups Γ, in an attempt to generalize the toroidal compactifications of Ash-Mumford-Rapoport-Tai to non-classical cases. Their partial compactifications, which aim to fully compactify the images of period maps, rely on a choice of fan which is strongly compatible with Γ. In particular, they conjectured the existence of a complete fan, which would serve to simultaneously compactify all period maps of a given type.In this article, we briefly review the theory, and construct a fan which compactifies the image of a period map arising from a particular two-parameter family of Calabi-Yau threefolds studied by Hosono and Takagi, with Hodge numbers (1, 2, 2, 1). On the other hand, we disprove the existence of complete fans in some general cases, including the (1, 2, 2, 1) case.

show abstract

“…In particular, the constraint conditions that the representations are level 3 (see Subsection 1.3 for specific definition of level) and have first Hodge number h 3,0 = 1 ensure that we get Hodge representations associated to CY 3-fold type. For more background information, the reader might consult Section 1 and 2 of [HR20] as well as Appendix B of [Rob14]. In order to phrase our results, we assume a fixed torus and a fixed Weyl Chamber.…”

Section: Hodge Representations Associated To Cy 3-fold Typementioning

confidence: 99%

Hodge Representations of Calabi-Yau 3-fold Type

Han

2020

Preprint

Self Cite

View full text Add to dashboard Cite

In this thesis, I apply the Green-Griffiths-Kerr classification of Hodge representations to enumerate the Lie algebra Hodge representations of CY 3-fold type. IntroductionIn this thesis, we will complete the classification of real Hodge representations of Calabi-Yau 3-fold type that was begun in [FL13]. In the following subsections, we will introduce Hodge representation of Lie groups and Lie algebras, and the Hodge representation of Calabi-Yau 3-fold type. The introductory materials are mostly taken from [GGK12], [Rob14] and [HR20]. Hodge Representation on Lie group and Lie algebra LevelDefinition 1.1. An algebraic group is a group that is an algebraic variety, such that the multiplication and inversion operations are given by maps on the variety that are locally given by polynomials.Definition 1.2. A Hodge structure of weight n ∈ Z on a rational vector space V is a non-constant homomorphism φ : S 1 → Aut(V R ) of R-algebraic groups such that φ(−1) = (−1) n 1. The associated Hodge decomposition V C = ⊕ p+q=n V p,q with V p,q = V q,p is given by V p,q = {v ∈ V C |φ(z)v = z p−q v ∀z ∈ S 1 }.

show abstract

Hodge Representations

Cited by 5 publications

References 31 publications

Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

Extension of Period Maps by Polyhedral Fans

Hodge Representations of Calabi-Yau 3-fold Type

Contact Info

Product

Resources

About