Bounding volumes of singular fano threefolds

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let (X, Δ) be an n-dimensional ϵ-klt log ℚ-Fano pair. We give an upper bound for the volume Vol(X, Δ) = (-(KX + Δ))n when n = 2 , or n = 3 and X is ℚ-factorial of ρ(X)=1 . This bound is essentially sharp for . The main idea is to analyze the covering families of tigers constructed in J. McKernan (Boundedness of log terminal fano pairs of bounded index, preprint, 2002, arXiv:0205214). Existence of an upper bound for volumes is related to the Borisov-Alexeev-Borisov Conjecture, which asserts boundedness of the set of ϵ-klt log ℚ-Fano varieties of a given dimension.

Original languageEnglish
Pages (from-to)37-73
Number of pages37
JournalNagoya Mathematical Journal
Volume224
DOIs
Publication statusPublished - 2016 Dec 1

Fingerprint

Threefolds
Boundedness
Fano Variety
Upper bound
Factorial
n-dimensional
Covering
Family

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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title = "Bounding volumes of singular fano threefolds",
abstract = "Let (X, Δ) be an n-dimensional ϵ-klt log ℚ-Fano pair. We give an upper bound for the volume Vol(X, Δ) = (-(KX + Δ))n when n = 2 , or n = 3 and X is ℚ-factorial of ρ(X)=1 . This bound is essentially sharp for . The main idea is to analyze the covering families of tigers constructed in J.{\^A} McKernan (Boundedness of log terminal fano pairs of bounded index, preprint, 2002, arXiv:0205214). Existence of an upper bound for volumes is related to the Borisov-Alexeev-Borisov Conjecture, which asserts boundedness of the set of ϵ-klt log ℚ-Fano varieties of a given dimension.",
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Bounding volumes of singular fano threefolds. / Lai, Ching Jui.

In: Nagoya Mathematical Journal, Vol. 224, 01.12.2016, p. 37-73.

Research output: Contribution to journalArticle

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