TY - UNPB
T1 - Blowing up linear categories, refinements, and homological projective duality with base locus
AU - Jiang, Qingyuan
AU - Leung, Naichung Conan
N1 - 41 pages. Comments are welcome! v2: applications to CY fibrations added
PY - 2018/11/13
Y1 - 2018/11/13
N2 - In this paper, we first introduce geometric operations for linear categories, and as a consequence generalize Orlov's blow up formula [O04] to possibly singular local complete intersection centres. Second, we introduce refined blowing up of linear category along base--locus, and show that this operation is dual to taking linear section. Finally, as an application we produce examples of Calabi--Yau manifolds which admits Calabi--Yau categories fibrations over projective spaces.
AB - In this paper, we first introduce geometric operations for linear categories, and as a consequence generalize Orlov's blow up formula [O04] to possibly singular local complete intersection centres. Second, we introduce refined blowing up of linear category along base--locus, and show that this operation is dual to taking linear section. Finally, as an application we produce examples of Calabi--Yau manifolds which admits Calabi--Yau categories fibrations over projective spaces.
KW - math.AG
M3 - Working paper
BT - Blowing up linear categories, refinements, and homological projective duality with base locus
PB - ArXiv
ER -