The Nonvanishing Problem for varieties with nef anticanonical bundle
Documenta mathematica, Tome 28 (2023) no. 6, pp. 1393-1440
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We prove that if (X,Δ) is a threefold pair with mild singularities such that −(KX+Δ) is nef, then the numerical class of −(KX+Δ) is effective.
Classification :
14E30
Mots-clés : generalised Nonvanishing Conjecture, nef anticanonical sheaf, Minimal Model Program
Mots-clés : generalised Nonvanishing Conjecture, nef anticanonical sheaf, Minimal Model Program
@article{10_4171_dm_936,
author = {Vladimir Lazi\'c and Shin-ichi Matsumura and Thomas Peternell and Nikolaos Tsakanikas and Zhixin Xie},
title = {The {Nonvanishing} {Problem} for varieties with nef anticanonical bundle},
journal = {Documenta mathematica},
pages = {1393--1440},
publisher = {mathdoc},
volume = {28},
number = {6},
year = {2023},
doi = {10.4171/dm/936},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/936/}
}
TY - JOUR AU - Vladimir Lazić AU - Shin-ichi Matsumura AU - Thomas Peternell AU - Nikolaos Tsakanikas AU - Zhixin Xie TI - The Nonvanishing Problem for varieties with nef anticanonical bundle JO - Documenta mathematica PY - 2023 SP - 1393 EP - 1440 VL - 28 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4171/dm/936/ DO - 10.4171/dm/936 ID - 10_4171_dm_936 ER -
%0 Journal Article %A Vladimir Lazić %A Shin-ichi Matsumura %A Thomas Peternell %A Nikolaos Tsakanikas %A Zhixin Xie %T The Nonvanishing Problem for varieties with nef anticanonical bundle %J Documenta mathematica %D 2023 %P 1393-1440 %V 28 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4171/dm/936/ %R 10.4171/dm/936 %F 10_4171_dm_936
Vladimir Lazić; Shin-ichi Matsumura; Thomas Peternell; Nikolaos Tsakanikas; Zhixin Xie. The Nonvanishing Problem for varieties with nef anticanonical bundle. Documenta mathematica, Tome 28 (2023) no. 6, pp. 1393-1440. doi: 10.4171/dm/936
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