A generalization of Δ-genus for big divisors on projective varieties. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Fukuma, Yoshiaki
• Is Part Of: Communications in algebra. Volume 48:Issue 1(2020)
• Page Start: 168
• Page End: 184
• Publication Date: 2020-01-02
• Subjects: Big divisors -- Δ-genus -- volume -- Okounkov body; Primary 14C20 -- Secondary 52B20; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1635609
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let X be a complex projective variety, and let D be a big Cartier divisor on X. For this data, we define an invariant Δ b ( X, D ) that refines the Δ-genus introduced by Fujita for nef and big divisors. We relate Δ b ( X, D ) to the Okounkov body of D, and give some examples. In particular, we show that Δ b ( X, D ) can be arbitrarily negative already on surfaces.