The vanishing theorems

By S. Mardešić. 2000

298 citations recorded by the source corpus.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/abca7748e8976023e59fd90d07e9b9e7eeaa26fc

How researchers see this paper

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In Geometry and Topology

1. Carlos Simpson
2. Xiaokui Yang
3. Kefeng Liu
4. O. Fujino
5. Constantin Shramov
6. K. Matsuki
7. Hsin-Ju Wang
8. Y. Siu

Citations in the corpus

• Multiplier ideal sheaves in complex and algebraic geometry (2005, background): “If we have a parametrized version of the minimal model conjecture, then we have the answer([26]), because pluricanonical sections are independent of blowing-ups and blowing-downs and the minimal models have numerically effective canonical line bundles for which the theorem of Kawamata-Viehweg([27,28”
• Explicit birational geometry of threefolds of general type (2007, unknown): “{(1, 2), (9, 23), }, K3 = 1 46 , m0 = 8.”
• Hyperelliptic and trigonal Fano threefolds (2004, methodology): “The following result is implied by the Riemann–Roch theorem (see [15], [17], [88]), the Kawamata–Viehweg vanishing theorem (see [91], [120]), the rationality of canonical singularities (see [93], [96]), and the global-to-local spectral sequence.”
• A sharp bound for the Castelnuovo–Mumford regularity of subspace arrangements (2001, background): “However, for an ideal I corresponding to a smooth variety in characteristic zero, the regularity of I is linear in terms of geometric data ([2,5,14,15,18]).”
• Kawamata-Viehweg vanishing as Kodaira vanishing for stacks (2002, methodology): “In addition, we explain, using the stack X, how the Kawamata–Viehweg vanishing theorem ([4], [7], [11]) can naturally be interpreted as an application of Kodaira vanishing for stacks.”
• A TRANSCENDENTAL APPROACH TO KOLL AR'S INJECTIVITY THEOREM II (2007, background): “We note that the arguments in [11], [12], [14], [15], and [16] are geometric.”
• Local Systems on Proper Algebraic V -manifolds (2010, methodology): “I first learned about this kind of idea when reading Viehweg’s paper [108], even though his technical approach, investigating further the singularities of purely cyclic coverings arising from the crossing points, is different from Kawamata’s.”