Exotic surfaces

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dc.contributor.authorReyes, Javier
dc.contributor.authorUrzua, Giancarlo
dc.date.accessioned2025-01-20T16:14:55Z
dc.date.available2025-01-20T16:14:55Z
dc.date.issued2024
dc.description.abstractAlthough exotic blow-ups of the projective plane at n points have been constructed for every n >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \ge 2$$\end{document}, the only examples known by means of rational blowdowns satisfy n >= 5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \ge 5$$\end{document}. It has been an intriguing problem whether it is possible to decrease n. In this paper, we construct the first exotic CP2#4CP2<overline>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}{\mathbb {P}}<^>2 \# 4 \overline{{\mathbb {C}}{\mathbb {P}}<^>2}$$\end{document} with this technique. We also construct exotic 3CP2#b-CP2<overline>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3{\mathbb {C}}{\mathbb {P}}<^>2 \# b<^>- \overline{{\mathbb {C}}{\mathbb {P}}<^>2}$$\end{document} for b-=9,8,7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b<^>-=9,8,7$$\end{document}. All of them are minimal and symplectic, as they are produced from projective surfaces W with Wahl singularities and KW\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_W$$\end{document} big and nef. In more generality, we elaborate on the problem of finding exotic (2 chi(OW)-1)CP2#(10 chi(OW)-KW2-1)CP2<overline>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} (2\chi ({\mathcal {O}}_W)-1) {\mathbb {C}}{\mathbb {P}}<^>2 \# (10\chi ({\mathcal {O}}_W)-K<^>2_W-1) \overline{{\mathbb {C}}{\mathbb {P}}<^>2} \end{aligned}$$\end{document}from these Koll & aacute;r-Shepherd-Barron-Alexeev surfaces W, obtaining explicit geometric obstructions on the corresponding configurations of rational curves.
dc.fuente.origenWOS
dc.identifier.doi10.1007/s00208-024-02916-7
dc.identifier.eissn1432-1807
dc.identifier.issn0025-5831
dc.identifier.urihttps://doi.org/10.1007/s00208-024-02916-7
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/90467
dc.identifier.wosidWOS:001248592600001
dc.language.isoen
dc.revistaMathematische annalen
dc.rightsacceso restringido
dc.titleExotic surfaces
dc.typeartículo
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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