Computing isolated orbifolds in weighted flag varieties. (March 2017)

• Record Type: Journal Article
• Authors: Qureshi, Muhammad Imran
• Is Part Of: Journal of symbolic computation. Volume 79(2017)Part 2
• Page Start: 457
• Page End: 474
• Publication Date: 2017-03
• Subjects: Weighted flag varieties -- Isolated orbifolds -- Complete intersections -- Fano 3-folds -- Calabi–Yau 3-folds; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.02.018
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Given a weighted flag variety w Σ ( μ, u ) corresponding to chosen fixed parameters μ and u, we present an algorithm to compute lists of all possible projectively Gorenstein n -folds, having canonical weight k and isolated orbifold points, appearing as weighted complete intersections in w Σ ( μ, u ) or some projective cone(s) over w Σ ( μ, u ) . We apply our algorithm to compute lists of interesting classes of polarized 3-folds with isolated orbifold points in the codimension 8 weighted G 2 variety. We also show the existence of some families of log-terminal Q -Fano 3-folds in codimension 8 by explicitly constructing them as quasilinear sections of a weighted G 2 -variety.