Ars Mathematica

I’m going to be far from the Internet starting on Monday, so I’ve asked sigfpe — of comment board and Neighborhood of Infinity fame — to help fill in for me.

Rick Miranda has written the clearest introduction to the algebraic geometry’s linear systems I’ve ever seen, in his article Linear Systems of Plane Curves from the February 1999 Notices of the AMS. He’s also written a much more technical article on algebraic surfaces which provides a good summary of the different classes of the Enriques classification.

I spotted this paper, Multiple polylogarithms, polygons, trees and algebraic cycles, on ArXiv. It relates the values of certain iterated integrals to incredibly complex and abstract objects in algebraic geometry.

Chris Peters has written two introductions to the classification of complex algebraic surfaces: a long version and a short one. The long version introduces the necessary background in complex manifolds and sheaf cohomology, while the short one skips right to the Enriques classification.

It’s the beginning of the month and the solution to last month’s Ponder This challenge is up, as well as the puzzle for August:

For K as large as possible, produce a K-digit integer M such that for each N=1,2,…,K, the integer given by the first N digits of M is divisible by N.
An example is K=4, M=7084, because 7 is divisible by 1; 70 is divisible by 2; 708 is divisible by 3; and 7084 is divisible by 4.

I guess that the largest K is around 28.