Kawamata-Viehweg vanishing as Kodaira vanishing for stacks

By K. Matsuki, Martin Olsson. 2002

71 citations recorded by the source corpus.

We associate to a pair $(X,D)$, consisting of a smooth scheme with a divisor $D\in \text{Div}(X)\otimes \mathbb{Q}$ whose support is a divisor with normal crossings, a canonical Deligne--Mumford stack over $X$ on which $D$ becomes integral. We then reinterpret the Kawamata--Viehweg vanishing theorem as Kodaira vanishing for stacks.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ca49cd430d963b2972afa48fe70bc04279e33e19

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Citations in the corpus

Hodge theoretic aspects of mirror symmetry (2008, background): “Conceptually the best way to define the stack Z is as a moduli stack classifying (special) log structures associated with X , the divisor D and the number N (see [MO05] for the details).”
Using stacks to impose tangency conditions on curves (2003, background): “w these two stacks can diﬀer is to let Dbe a reducible conic in X= P2. If D 1 and D 2 areitsirreducible components andone takes r 1 = r 2 = r, then XD,~r (Deﬁnition 2.6) is isomorphic to the stack of [MO]. Over the node of D, there are two factors of µr acting, whereas in XD,r there is only one. Whi”
$F$-zips with additional structure (2012, background): “Then in [14] there is attached a morphism X → X, where X is a smooth proper Deligne-Mumford stack which is the “minimal covering” of X such that D becomes integral.”
Parabolic sheaves on logarithmic schemes (2010, background): “We would like to thank Luc Illusie, Arthur Ogus, and Martin Olsson for useful conversations.”
Katz's middle convolution algorithm (2006, unknown): “for every point qi the parabolic type is a divisor concentrated over roots of unity in S(1), then as discussed in [16] [24] [105] [74], the parabolic bundle may also be viewed as a bundle on a Deligne-Mumford stack Z[ m ] obtained by assigning an integer m to the points qi.”
Local Systems on Proper Algebraic V -manifolds (2010, methodology): “In current-day terms, Matsuki and Olsson have explained it as an instance of Kodaira vanishing over a root stack [68].”
Hodge theoretic aspects of mirror symmetry (2008, background): “Conceptually the best way to define the stack Z is as a moduli stack classifying (special) log structures associated with X, the divisor D and the number N (see [MO05] for the details).”