Positivity in algebraic geometry

By R. Lazarsfeld. 2004

2,238 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/4ab74f65af82281e7ecd7cc90968e7c8e59ad421

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In Algebra and Number Theory

In Geometry and Topology

In Theoretical Computer Science

Citations in the corpus

Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds (2012, methodology): “We refer the reader to Lazarsfeld’s book [62] for a comprehensive treatment of positivity for line bundles.”
Jet schemes and singularities (2006, background): “For basic facts about integral closure of ideals, see for example [Laz], §9.”
Toric plurisubharmonic functions and analytic adjoint ideal sheaves (2010, background): “urface, say H. This ideal, wellknown in complex algebraic geometry, is a subsheaf of the multiplier ideal sheaf which measures how largely the restricted ideal J(a)|H contains J(a|H), as expressed in [Laz04]. Our goal is to deﬁne an analytic analogue AdjH(ϕ) attached to any psh function on a smooth ”
Unitary local systems, multiplier ideals, and polynomial periodicity of Hodge numbers (2006, background): “Multiplier ideals. We review the definition of multiplier ideals and the local vanishing theorem ([ La ]).”
Big rational surfaces (2009, background): “Recall that a (real) divisor B on X is big if there are an ample divisor A and an effective divisor E on X such that B is numerically equivalent to A + E. An integral divisor B on X is semi-ample if there is a positive integer n such that the linear system | nB | is base point free. See [ 20, Chapte”
Contact loci in arc spaces (2003, background): “Recall that a graded sequence of ideals is a set of ideals a• = {ap}p≥1 such that ap � aq ⊆ ap+q for all p and q (see [ Laz ] for more on this topic).”
A study of the Hilbert-Mumford criterion for the stability of projective varieties (2004, methodology): “ned in E2 then (π∗L −ǫE1).C = (π∗L −ǫE).C + ǫE2.C ≥0. Hence by the Kleiman criterion, π∗L−ǫE1 is nef. But this line bundle is the pullback of L−ǫE1 from BlZ1 X, so the latter line bundle is also nef ([La] Example 1.4.3(ii)), proving that ǫ ≤ǫ(Z1). Lemma 4.28. Let (X,L) be a smooth polarised variety ”
GV-sheaves, Fourier-Mukai transform, and generic vanishing (2006, methodology): “[ La ], Theorem 11.2.23), we have that J (k Lk) =J (k Lk).”
On the Cohomology of Pseudoeffective Line Bundles (2014, background): “Many related questions are discussed in the algebraic setting in Lazarfeld’s book [Laz04].”