Blown-Up Hirzebruch Surfaces and Special Divisor Classes
- 주제(키워드) Hirzebruch surface , monoidal transformation , special divisor
- 주제(기타) Mathematics
- 설명문(일반) [Lee, Jae-Hyouk] Ewha Womans Univ, Dept Math, Seoul 120750, South Korea; [Shin, YongJoo] Chungnam Natl Univ, Dept Math, Sci Bldg 1,99 Daehak Ro, Daejeon, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 gold, Green Submitted
- 발행기관 MDPI
- 발행년도 2020
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000172382
- 본문언어 영어
- Published As https://dx.doi.org/10.3390/math8060867
초록/요약
We work on special divisor classes on blow-ups F-p,(r) of Hirzebruch surfaces over the field of complex numbers, and extend fundamental properties of special divisor classes on del Pezzo surfaces parallel to analogous ones on surfaces F-p,F-r. We also consider special divisor classes on surfaces F-p,(r) with respect to monoidal transformations and explain the tie-ups among them contrast to the special divisor classes on del Pezzo surfaces. In particular, the fundamental properties of quartic rational divisor classes on surfaces F-p,F-r are studied, and we obtain interwinded relationships among rulings, exceptional systems and quartic rational divisor classes along with monoidal transformations. We also obtain the effectiveness for the rational divisor classes on F-p,F-r with positivity condition.
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