caa a22 4500 445869518 CHVBK 20180317145507.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00605-010-0242-8 doi (NATIONALLICENCE)springer-10.1007/s00605-010-0242-8 Yasufuku Yu Graduate Center of The City University of New York, 365 Fifth Ave., 10016, New York, NY, USA aut Vojta's conjecture on blowups of $${\mathbb{P}^n}$$, greatest common divisors, and the abc conjecture [Elektronische Daten] [Yu Yasufuku] We will prove some cases of Vojta's conjecture on blowups of $${\mathbb{P}^n}$$, using Schmidt's subspace theorem. The results can be stated as inequalities of greatest common divisors. Moreover, from Vojta's conjecture on one further blowup at an infinitely near point, we derive a still-open special case of the abc-conjecture. Springer-Verlag, 2010 Vojta's conjecture nationallicence Subspace theorem nationallicence Greatest common divisors nationallicence Blowups nationallicence abc Conjecture nationallicence Monatshefte für Mathematik Springer Vienna 163/2(2011-06-01), 237-247 0026-9255 163:2<237 2011 163 605 https://doi.org/10.1007/s00605-010-0242-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0242-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Yasufuku Yu Graduate Center of The City University of New York, 365 Fifth Ave., 10016, New York, NY, USA aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 163/2(2011-06-01), 237-247 0026-9255 163:2<237 2011 163 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer