Let (X,L) be a smooth polarized variety of dimension n. Let A \in |L| be an irreducible hypersurface and let \Sigma be the singular locus of A. We assume that \Sigma is a smooth subvariety of dimension k \geq 2, and odd codimension \geq 3. Motivated from the result of Beltrametti et al. (J. Math. Soc. Japan; to appear), we study the nefness and bigness of the adjoint bundle K_{\Sigma}+(k-2)L_{\Sigma} in this framework. Sevferal explicit examples show that the results are effective.
Adjunction and singular loci of hyperplane sections, II / M. C. Beltrametti, A. Lanteri, A.J. Sommese. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 0009-725X. - 63:2(2014 May), pp. 247-255. [10.1007/s12215-014-0155-9]
Adjunction and singular loci of hyperplane sections, II
A. LanteriSecondo
;
2014
Abstract
Let (X,L) be a smooth polarized variety of dimension n. Let A \in |L| be an irreducible hypersurface and let \Sigma be the singular locus of A. We assume that \Sigma is a smooth subvariety of dimension k \geq 2, and odd codimension \geq 3. Motivated from the result of Beltrametti et al. (J. Math. Soc. Japan; to appear), we study the nefness and bigness of the adjoint bundle K_{\Sigma}+(k-2)L_{\Sigma} in this framework. Sevferal explicit examples show that the results are effective.
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