Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under Kähler deformation

Hwang, Jun-Muk; Mok, Ngaiming

doi:10.1007/s00222-004-0417-9

Cited by 58 publications

(73 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The proof of (ii) is the same as that of Proposition 2.3.1 in [HM05]. The proof of (iii) and (iv) is a modification of that of Theorem 1.1.3 (iii) in [HM05]. In fact, fix α ∈Ŝ outside the zero locus of λ A and pick any α ′ ∈ T α (Ŝ).…”

Section: Its Prolongation Aut(ŝ)mentioning

confidence: 97%

“…Theorem 2.3 ( [HM05], Theorem 1.1.2). Let S PV be an irreducible nonsingular non-degenerate subvariety.…”

Section: Its Prolongation Aut(ŝ)mentioning

confidence: 99%

“…In [HM05], some partial results on the structure of such varieties were obtained. Here we collect them with some immediate improvements.…”

Section: Its Prolongation Aut(ŝ)mentioning

confidence: 99%

“…More precisely, for a projective subvariety S P(V ), consider the Lie algebra aut(Ŝ) ⊂ gl(V ) of infinitesimal linear automorphisms of the affine coneŜ. [HM05] shows that one can study prolongations aut(Ŝ) (k) using projective geometry of S ⊂ PV and the deformation theory of rational curves on S. Combining these two geometric tools, the following generalization of Theorem 1.1 (1) is proved in Theorem 1.1.2 of [HM05]. Theorem 1.2.…”

Section: Introductionmentioning

confidence: 99%

“…It will be proved in Section 7 and Section 8. Many of the geometric ideas in these two sections are borrowed from Section 6 and Section 8 of [HM05]. However, the main line of arguments and details of the proof are rather different from [HM05], except Propositions 7.6 and 8.6 whose proofs are essentially contained in those of Proposition 6.3.4 and Proposition 8.3.4 of [HM05], respectively.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Classification of non-degenerate projective varieties with non-zero prolongation and application to target rigidity

Hwang

2011

Invent. math.

Self Cite

View full text Add to dashboard Cite

Abstract. The prolongation g (k) of a linear Lie algebra g ⊂ gl(V ) plays an important role in the study of symmetries of G-structures. Cartan and Kobayashi-Nagano have given a complete classification of irreducible linear Lie algebras g ⊂ gl(V ) with non-zero prolongations.If g is the Lie algebra aut(Ŝ) of infinitesimal linear automorphisms of a projective variety S ⊂ PV , its prolongation g (k) is related to the symmetries of cone structures, an important example of which is the variety of minimal rational tangents in the study of uniruled projective manifolds. From this perspective, understanding the prolongation aut(Ŝ) (k) is useful in questions related to the automorphism groups of uniruled projective manifolds. Our main result is a complete classification of irreducible non-degenerate nonsingular variety S ⊂ PV with aut(Ŝ) (k) = 0, which can be viewed as a generalization of the result of Cartan and Kobayashi-Nagano.As an application, we show that when S is linearly normal and Sec(S) = PV , the blow-up Bl S (PV ) has the target rigidity property, i.e., any deformation of a surjective morphism f : Y → Bl S (PV ) comes from the automorphisms of Bl S (PV ).

show abstract

Section: Its Prolongation Aut(ŝ)mentioning

confidence: 97%

“…Theorem 2.3 ( [HM05], Theorem 1.1.2). Let S PV be an irreducible nonsingular non-degenerate subvariety.…”

Section: Its Prolongation Aut(ŝ)mentioning

confidence: 99%

“…In [HM05], some partial results on the structure of such varieties were obtained. Here we collect them with some immediate improvements.…”

Section: Its Prolongation Aut(ŝ)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Classification of non-degenerate projective varieties with non-zero prolongation and application to target rigidity

Hwang

2011

Invent. math.

Self Cite

View full text Add to dashboard Cite

show abstract

Legendrian Cone Structures and Contact Prolongations

Hwang

2021

Geometry, Lie Theory and Applications

View full text Add to dashboard Cite

We exploit a natural correspondence between holomorphic (2, 3, 5)-distributions and nondegenerate lines on holomorphic contact manifolds of dimension 5 to present a new perspective in the study of symmetries of (2, 3, 5)-distributions. This leads to a number of new results in this classical subject, including an unexpected relation between the multiply-transitive families of models having 7-and 6-dimensional symmetries, and a one-to-one correspondence between equivalence classes of nontransitive (2, 3, 5)-distributions with 6-dimensional symmetries and nonhomogeneous nondegenerate Legendrian curves in P 3 . An ingredient for establishing the former is an explicit classification of homogeneous nondegenerate Legendrian curves in P 3 , which we present.

show abstract

Geometric Structures and Substructures on Uniruled Projective Manifolds

Mok

2016

Foliation Theory in Algebraic Geometry

View full text Add to dashboard Cite

Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under Kähler deformation

Cited by 58 publications

References 20 publications

Classification of non-degenerate projective varieties with non-zero prolongation and application to target rigidity

Classification of non-degenerate projective varieties with non-zero prolongation and application to target rigidity

Legendrian Cone Structures and Contact Prolongations

Geometric Structures and Substructures on Uniruled Projective Manifolds

Contact Info

Product

Resources

About