Higher direct images of log canonical divisors

By O. Fujino. 2004

59 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e34fc5795b66bf6a5446d8ab7fc249d1b7ed5603

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In Algebra and Number Theory

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Citations in the corpus

Positivity of twisted relative pluricanonical bundles and their direct images (2014, background): “Actually this field has generated many important works, including the twisted case by a semi-ample line bundle L; we will only mention here a few of them [1], [7], [18], [22], [24], [25], [26], [28], [29], [32], [33], [34], [47] (and we apologize to the authors we omit .”
Fundamental Theorems for the Log Minimal Model Program (2009, background): “ 0. By induction, we see that Rif ∗OV (D−S) = 0 and Rif∗OS(D) = 0 for every i>0. Thus, we have Rif ∗OV (D) = 0 for i>0. The next theorem is the main theorem of this section (cf. [A1]). See also [F3]. Theorem 6.3 (Torsion-freeness and vanishing theorem). Let Y be a smooth variety and let Bbe a ”
Hodge metrics and the curvature of higher direct images (2007, unknown): “eralized by Fujita [Ft], Kawamata [Ka1], Viehweg [Vi1], Koll´ar [Ko1], and so on, in more algebro-geometric setting. There are also positivity results on higher direct images by Moriwaki [Mw], Fujino [Fn] and so on. We refer to [Mr][EV][Vi2][Ko2] for further remarks on related results. On the analyt”
Existence of log canonical closures (2011, background): “puted from X′ → Y commutes with any pull back in the sense of [Koll´ar07, 8.4.9(3)]. Since J is deﬁned by a variation of mixed Hodge structures (cf. [Koll´ar07, 8.4.5(7)]), its g-nefness follows from [Fujino04] or [Kawamata10, 25]. We need the following simple lemma. Lemma 2.2. Let h: X→ Y and h′ : ”
Introduction to the log minimal model program for log canonical pairs (2009, background): “= 0 for any q<dimX. Remark 2.44. We can see that Corollary 2.43 is contained in [F4, Theorem 2.6], which is a very special case of Theorem 2.39 (ii). I forgot to state Corollary 2.43 explicitly in [F4]. There, we do not need embedded simple normal crossing pairs. We note that there are typos in t”
Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, unknown): “We omit the proof because it is routine work. See, for example, [ F1 , Section 2.2].”