Log Terminal Singularities

Chiecchio, Alberto; Urbinati, Stefano

doi:10.48550/arxiv.1211.6235

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Fano Varieties1

Log Terminal Singularities1

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2014

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“…In [CU12, 5.2], the notion of log terminal + singularities was introduced: if X is a normal variety over C, X has lt + singularities if for one (equivalently all) log resolution f : Y → X, K Y + f * (−K X ) has coefficients strictly bigger than −1 (for any prime component of the exceptional divisor). By [CU12,5.15], if X has lt + singularities, than is has klt singularities (in the sense of the above theorem) if and only if R(X, −K X ) is finitely generated. Thus the above theorem is true under the hypothesis that X has only lt + singularities.…”

Section: Fano Varietiesmentioning

confidence: 99%

Ample Weil divisors

Chiecchio

Urbinati

2015

Journal of Algebra

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Section: Fano Varietiesmentioning

confidence: 99%

Ample Weil divisors

Chiecchio

Urbinati

2015

Journal of Algebra

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“…In this section we recall some definitions and results due to [dFH09] (we will use the notation of [CU12]). Subsequently, we prove generalizations of well-known results.…”

Section: Log Terminal Singularitiesmentioning

confidence: 99%

About a Minimal Model Program without flips

Chiecchio

2014

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We introduce a new vector space associated to a projective variety, the Weil Néron-Severi space, which we show is finitely generated and contains the usual Néron-Severi space as a subspace. We define the Nef cone of Weil divisor and the cone of Weil curves. We study these cones, and prove a new Cone theorem. We use this theorem to describe a Minimal Model Program without flips. Contents 1. Introduction 1 Aknowledgments 4 2. Of Weil divisors (and other sorrows) 4 2.1. Weil divisors and valuations 4 2.2. Positivity for Weil divisors 6 3. Log terminal singularities 9 4. The Weil Néron-Severi space 12 5. The Weil nef cone and the cone of Weil curves 17 6. The Cone theorem 20 7. The program 24 8. The relative statements 26 References 28

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Log Terminal Singularities

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Ample Weil divisors

Ample Weil divisors

About a Minimal Model Program without flips

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