Rendiconti del Seminario Matematico della Università di Padova

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Volume 121, 2009, pp. 93–119
DOI: 10.4171/RSMUP/121-6

Sectional Invariants of Scroll over a Smooth Projective Variety

Yoshiaki Fukuma[1]

(1) Kochi University, Japan

Let X be a smooth complex variety of dimension n and let E be an ample vector bundle of rank r on X. Then we calculate the ith sectional Euler number ei(PX(E),H(E)) for i ≥ 2n - 3 or i = 1, and the ith sectional Hodge number of type (j,i - j) hi i-j(PX(E),H(E)) for i ≥ 2n - 1 and 0 ≤ ji, where PX(E) is the projective space bundle associated with E and H(E) is its tautological line bundle. Moreover we define a new invariant v(X,E) for rn - 1. This invariant is thought to be a generalization of curve genus. We will investigate some properties of this invariant.

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Fukuma Yoshiaki: Sectional Invariants of Scroll over a Smooth Projective Variety. Rend. Sem. Mat. Univ. Padova 121 (2009), 93-119. doi: 10.4171/RSMUP/121-6