Principles of Algebraic Geometry

Griffiths, Phillip; Harris, Joe

doi:10.1002/9781118032527

Cited by 2,790 publications

(4,188 citation statements)

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“…fact that the Lefschetz hyperplane theorem ensures that in the gauged linear σ-model of the quintic the generator of H 2 (CP 4 , Z) of the ambient projective space, CP 4 , induces the generator of H 2 (Quintic, Z) on the quintic hyperplane [50].…”

Section: Jhep02(2007)006mentioning

confidence: 99%

D-brane monodromies from a matrix-factorization perspective

Jockers

2007

J. High Energy Phys.

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Section: Jhep02(2007)006mentioning

confidence: 99%

D-brane monodromies from a matrix-factorization perspective

Jockers

2007

J. High Energy Phys.

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“…Recall that we use cohomology with rational coefficients. A standard textbook reference for what follows is [92]; see also [175,44].…”

Section: Overviewmentioning

confidence: 99%

“…Chern gave a proof of the hard Lefschetz in the 1950's (see [92]) which still relies on Hodge theory and exploits the action of sl 2 (C) on the differential forms on a Kähler manifold.…”

Section: Historical and Other Remarksmentioning

confidence: 99%

The decomposition theorem, perverse sheaves and the topology of algebraic maps

Andrea

Migliorini

2009

Bull. Amer. Math. Soc.

163

152

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We give a motivated introduction to the theory of perverse sheaves, culminating in the decomposition theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the theory develops naturally from classical constructions used in the study of topological properties of algebraic varieties. While most proofs are omitted, we discuss several approaches to the decomposition theorem, indicate some important applications and examples.

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“…In these books, schemes played the central role. In the late 1970s, books by Hartshorne [12], Griffiths and Harris [9], and Shafarevich [21] were published. In comparison to EGA, these books are user-friendly, but they still require a substantial background.…”

Section: Learning Algebraic Geometry Imentioning

confidence: 99%