Euler and algebraic geometry

Totaro, Burt

doi:10.1090/s0273-0979-07-01178-0

Cited by 6 publications

(3 citation statements)

References 28 publications

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“…One can show (cf. [Tot12]) that S has a unique elliptic fibration S → P 1 , induced by some nef line bundle L, and infinitely many smooth rational curves, each of which is a section of S → P 1 . The ray spanned by L in Nef(S) is extremal, and is the only extremal ray of square 0 of the nef cone.…”

Section: Examplesmentioning

confidence: 99%

Boucksom–Zariski and Weyl Chambers on Irreducible Holomorphic Symplectic Manifolds

Denisi

2022

International Mathematics Research Notices

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Inspired by the work of Bauer, Küronya, and Szemberg, we provide for the big cone of a projective irreducible holomorphic symplectic (IHS) manifold a decomposition into chambers (which we describe in detail), in each of which the support of the negative part of the divisorial Zariski decomposition is constant. We see how the obtained decomposition of the big cone allows to describe the volume function. Moreover, similarly to the case of surfaces, we see that the big cone of a projective IHS manifold admits a decomposition into simple Weyl chambers, which we compare to that induced by the divisorial Zariski decomposition. To conclude, we determine the structure of the pseudo-effective cone.

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Section: Examplesmentioning

confidence: 99%

Boucksom–Zariski and Weyl Chambers on Irreducible Holomorphic Symplectic Manifolds

Denisi

2022

International Mathematics Research Notices

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“…Both this book by Christian Houzel and the book [33] by Jeremy Gray contain a wealth of information about the early history of elliptic and hypergeometric functions, and of differential equations in general. See also the very nice expository paper [66] by Burt Totaro.…”

Section: Differential Equations and Algebraic Geometrymentioning

confidence: 99%

The arithmetic and topology of differential equations

Zagier

2018

European Congress of Mathematics

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“…In particular, Katz’s theorem that rigid local systems over the orbifold projective line are of geometric origin, does not give smooth geometric origin. The discussion of the notion of geometric origin in [Tot07] should probably be modified accordingly.…”

Section: Preliminariesmentioning

confidence: 99%