Abstract. Let X be a non-singular quasi-projective variety over a field, and let E be a vector bu... more Abstract. Let X be a non-singular quasi-projective variety over a field, and let E be a vector bundle over X . Let GX(d, E) be the Grassmann bundle of E overX parametrizing corank d subbundles of E with projection π : GX(d, E) → X , and let Q ← π ∗E be the universal quotient bundle of rank d. In this article, a closed formula for π∗ ch(detQ), the push-forward of the Chern character of the Plücker line bundle detQ by π is given in terms of the Segre classes of E . Our formula yields a degree formula for GX(d, E) with respect to detQ when X is projective and ∧E is very ample. To prove the formula above, a push-forward formula in the Chow rings from a partial flag bundle of E to X is given.
An adjoint variety X(g)associated to a complex simple Lie algebra is by definition a projective v... more An adjoint variety X(g)associated to a complex simple Lie algebra is by definition a projective variety in ℙ*(g) obtained as the projectivization of the (unique) non-zero, minimal nilpotent orbit in g. We first describe the tangent loci of X(g) in terms of triples. Secondly for a graded decomposition of contact type we show that the intersection of X(g) and the linear subspace ℙ*(g1) in ℙ*(g) coincides with the cubic Veronese variety associated to g.
Abstract. Let X be a non-singular quasi-projective variety over a field, and let E be a vector bu... more Abstract. Let X be a non-singular quasi-projective variety over a field, and let E be a vector bundle over X . Let GX(d, E) be the Grassmann bundle of E overX parametrizing corank d subbundles of E with projection π : GX(d, E) → X , and let Q ← π ∗E be the universal quotient bundle of rank d. In this article, a closed formula for π∗ ch(detQ), the push-forward of the Chern character of the Plücker line bundle detQ by π is given in terms of the Segre classes of E . Our formula yields a degree formula for GX(d, E) with respect to detQ when X is projective and ∧E is very ample. To prove the formula above, a push-forward formula in the Chow rings from a partial flag bundle of E to X is given.
An adjoint variety X(g)associated to a complex simple Lie algebra is by definition a projective v... more An adjoint variety X(g)associated to a complex simple Lie algebra is by definition a projective variety in ℙ*(g) obtained as the projectivization of the (unique) non-zero, minimal nilpotent orbit in g. We first describe the tangent loci of X(g) in terms of triples. Secondly for a graded decomposition of contact type we show that the intersection of X(g) and the linear subspace ℙ*(g1) in ℙ*(g) coincides with the cubic Veronese variety associated to g.
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Papers by hajime kaji