On delta complex structures of complex quasi-projective varieties - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T00:49:14Z http://mathoverflow.net/feeds/question/68657 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/68657/on-delta-complex-structures-of-complex-quasi-projective-varieties On delta complex structures of complex quasi-projective varieties Hugo Chapdelaine 2011-06-23T21:23:11Z 2011-06-25T15:45:20Z <p>Q1.Given a quasi-projective variety $X$ over $\mathbf{C}$, is it always possible to find a $\Delta$-complex structure on $X$?</p> <p>Q2. What is a good reference which gives a survey about what we know of $CW$-complex structures of quasi-projective varieties over $\mathbf{C}$?</p> http://mathoverflow.net/questions/68657/on-delta-complex-structures-of-complex-quasi-projective-varieties/68666#68666 Answer by Fernando Muro for On delta complex structures of complex quasi-projective varieties Fernando Muro 2011-06-23T22:05:41Z 2011-06-23T22:05:41Z <p>Actually, any complex algebraic variety can be triangulated as a <strong>pseudomanifold</strong>, which is a simplicial complex such that, if the variety has real dimension $n$, then any simplex is contained in an $n$-simplex, any $(n-1)$-simplex is contained in exactly two $n$-simplexes, and any two $n$-simplexes can be connected by a sequence of $n$-simplexes such that two consecutive ones share exactly one $(n-1)$-face.</p> http://mathoverflow.net/questions/68657/on-delta-complex-structures-of-complex-quasi-projective-varieties/68792#68792 Answer by Dan Ramras for On delta complex structures of complex quasi-projective varieties Dan Ramras 2011-06-25T15:45:20Z 2011-06-25T15:45:20Z <p>There are very general triangulability results for real (semi)algebraic sets (sets cut out by inequalities of real polynomials), and even for semianalytic and subanalytic sets. Lojasiewicz has some papers from the 60s on semianalytic sets; Hironaka and Hardt also have papers on the subject; and the book Real Algebraic Geometry by Bochnak, Coste, and Roy treats at least the semialgebraic case.</p>