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Characterization of Hermitian symmetric spaces by fundamental forms
 621–634. LIE ALGEBRA COHOMOLOGY, AND RIGIDITY 27
"... We show that an equivariantly embedded Hermitian symmetric space in a projective space which contains neither a projective space nor a hyperquadric as a component is characterized by its fundamental forms as a local submanifold of the projective space. Using some invarianttheoretic properties of th ..."
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We show that an equivariantly embedded Hermitian symmetric space in a projective space which contains neither a projective space nor a hyperquadric as a component is characterized by its fundamental forms as a local submanifold of the projective space. Using some invarianttheoretic properties of the fundamental forms and Seashi’s work on linear differential equations of finite type, we reduce the proof to the vanishing of certain Spencer cohomology groups. The vanishing is checked by Kostant’s harmonic theory for Lie algebra cohomology.
Differential geometry of submanifolds of projective space
 2006 IMA WORKSHOP “SYMMETRIES AND OVERDETERMINED SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS"
, 2006
"... These are lecture notes on the rigidity of submanifolds of projective space “resembling” compact Hermitian symmetric spaces in their homogeneous embeddings. The ..."
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Cited by 5 (2 self)
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These are lecture notes on the rigidity of submanifolds of projective space “resembling” compact Hermitian symmetric spaces in their homogeneous embeddings. The
Disproof of Modularity of Moduli Space of CY 3folds of Double covers of P3 ramified along eight planes
 in General Positions, math.arXiv,0709.1051
"... Abstract. We prove that the moduli space of CalabiYau 3folds coming from eight planes of P 3 in general positions is not modular. In fact we show the stronger statement that the Zariski closure of the monodromy group is actually the whole Sp(20, R). We construct an interesting submoduli, which we ..."
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Cited by 4 (2 self)
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Abstract. We prove that the moduli space of CalabiYau 3folds coming from eight planes of P 3 in general positions is not modular. In fact we show the stronger statement that the Zariski closure of the monodromy group is actually the whole Sp(20, R). We construct an interesting submoduli, which we call hyperelliptic locus, over which the weight 3 QHodge structure is the third wedge product of the weight 1 QHodge structure on the corresponding hyperelliptic curve. The nonextendibility of the hyperelliptic locus inside the moduli space of a genuine Shimura subvariety is proved. 1.
EXTERIOR DIFFERENTIAL SYSTEMS, LIE ALGEBRA COHOMOLOGY, AND THE RIGIDITY OF HOMOGENOUS VARIETIES
"... Abstract. These are expository notes from the 2008 Srni Winter School. They have two purposes: (1) to give a quick introduction to exterior differential systems (EDS), which is a collection of techniques for determining local existence to systems of partial differential equations, and (2) to give an ..."
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Abstract. These are expository notes from the 2008 Srni Winter School. They have two purposes: (1) to give a quick introduction to exterior differential systems (EDS), which is a collection of techniques for determining local existence to systems of partial differential equations, and (2) to give an exposition of recent work (joint with C. Robles) on the study of the FubiniGriffithsHarris rigidity of rational homogeneous varieties, which also involves an advance in the EDS technology.
DIFFERENTIAL GEOMETRY OF SUBMANIFOLDS OF PROJECTIVE SPACE
, 2006
"... Abstract. These are lecture notes on the rigidity of submanifolds of projective space “resembling” compact Hermitian symmetric spaces in their homogeneous embeddings. The results of ..."
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Abstract. These are lecture notes on the rigidity of submanifolds of projective space “resembling” compact Hermitian symmetric spaces in their homogeneous embeddings. The results of
EXTERIOR DIFFERENTIAL SYSTEMS, LIE ALGEBRA COHOMOLOGY, AND THE RIGIDITY OF HOMOGENOUS VARIETIES
, 802
"... Abstract. These are expository notes from the 2008 Srni Winter School. They have two purposes: (1) to give a quick introduction to exterior differential systems (EDS), which is a collection of techniques for determining local existence to systems of partial differential equations, and (2) to give an ..."
Abstract
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Abstract. These are expository notes from the 2008 Srni Winter School. They have two purposes: (1) to give a quick introduction to exterior differential systems (EDS), which is a collection of techniques for determining local existence to systems of partial differential equations, and (2) to give an exposition of recent work (joint with C. Robles) on the study of the FubiniGriffithsHarris rigidity of rational homogeneous varieties, which also involves an advance in the EDS technology.
CALABIYAU MANIFOLDS WHOSE MODULI SPACES ARE LOCALLY SYMMETRIC MANIFOLDS AND NO QUANTUM CORRECTIONS
, 806
"... Abstract. It is observed that there are a natural sequence of CY manifolds Mg that are double covers of CPg ramified over 2g + 2 hyperplanes and some of them are obtained from the Jacobian J(Cg) of hyperelliptic curve Cg by an action of an involution of a semidirect product of g−1 copies of groups ..."
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Abstract. It is observed that there are a natural sequence of CY manifolds Mg that are double covers of CPg ramified over 2g + 2 hyperplanes and some of them are obtained from the Jacobian J(Cg) of hyperelliptic curve Cg by an action of an involution of a semidirect product of g−1 copies of groups of order two with the symmetric group of g elements. This construction generalizes Kummer surfaces. We observed that the g2 KodairaSpencer classes on the Jacobian are invariant under the action of the above group. They form a basis of H1 “