Details
| Original language | English |
|---|---|
| Pages (from-to) | 1183-1207 |
| Number of pages | 25 |
| Journal | Annales Scientifiques de l'Ecole Normale Superieure |
| Volume | 53 |
| Issue number | 5 |
| Publication status | Published - 2020 |
Abstract
Keywords
- varieties of general type, minimal model program, boundedness results, topology of algebraic varieties
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Annales Scientifiques de l'Ecole Normale Superieure, Vol. 53, No. 5, 2020, p. 1183-1207.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the number and boundedness of log minimal models of general type
AU - Martinelli, Diletta
AU - Schreieder, Stefan
AU - Tasin, Luca
N1 - Funding Information: Parts of the results of this article were conceived when the third author was supported by the DFG Emmy Noether-Nachwuchsgruppe “Gute Strukturen in der höherdimensionalen birationalen Geometrie”. The second author is member of the SFB/TR 45 and thanks the Università Roma Tre for hospitality, where parts of this project were carried out.
PY - 2020
Y1 - 2020
N2 - We show that the number of marked minimal models of an n-dimensional smooth complex projective variety of general type can be bounded in terms of its volume, and, if n=3, also in terms of its Betti numbers. For an n-dimensional projective klt pair (X,D) with \(K_X+D\) big, we show more generally that the number of its weak log canonical models can be bounded in terms of the coefficients of D and the volume of \(K_X+D\). We further show that all n-dimensional projective klt pairs (X,D), such that \(K_X+D\) is big and nef of fixed volume and such that the coefficients of D are contained in a given DCC set, form a bounded family. It follows that in any dimension, minimal models of general type and bounded volume form a bounded family.
AB - We show that the number of marked minimal models of an n-dimensional smooth complex projective variety of general type can be bounded in terms of its volume, and, if n=3, also in terms of its Betti numbers. For an n-dimensional projective klt pair (X,D) with \(K_X+D\) big, we show more generally that the number of its weak log canonical models can be bounded in terms of the coefficients of D and the volume of \(K_X+D\). We further show that all n-dimensional projective klt pairs (X,D), such that \(K_X+D\) is big and nef of fixed volume and such that the coefficients of D are contained in a given DCC set, form a bounded family. It follows that in any dimension, minimal models of general type and bounded volume form a bounded family.
KW - varieties of general type
KW - minimal model program
KW - boundedness results
KW - topology of algebraic varieties
UR - http://www.scopus.com/inward/record.url?scp=85104300117&partnerID=8YFLogxK
U2 - 10.24033/ASENS.2443
DO - 10.24033/ASENS.2443
M3 - Article
VL - 53
SP - 1183
EP - 1207
JO - Annales Scientifiques de l'Ecole Normale Superieure
JF - Annales Scientifiques de l'Ecole Normale Superieure
SN - 0012-9593
IS - 5
ER -