4
$\begingroup$

I need a good reference about the connection between modular forms and line bundles. I found only Milne's note that treats briefly this argument. I've already checked, but without finding anything, many books such as:

  • "A first course in modular forms - F. Diamond, J. Shurman"
  • "Elliptic curves and modular forms - N.Koblitz"
  • "Modular Forms - Miyake"
  • "A course in arithmetic - J.P.Serre" (the last chapter)
  • "Complex analysis - E.Freitag, R.Busam"
  • 0
    Just to make sure, what exactly do you want to know that is not covered in Milne's notes?2012-09-24
  • 0
    The problem is the following: I took notes of the course, and the relation between line bundles and modular forms is a large enough subject (about 10 pages). Unfortunately these notes are not very clear, so I need some reference. Milne's note treats the subject in a single page.2012-09-24
  • 0
    To be more precise the argumets I need concerning: automorphy factors, classification of line bundles on $\mathcal H/\Gamma$ and modular forms...2012-09-24
  • 2
    There is not much substance to "line bundles versus modular forms"... mostly just a way of speaking, so don't look for any big mystery to be uncovered. In fact, the non-content is why many sources don't bother to speak in such terms.2012-09-25
  • 1
    ... more likely, a "non-modular" reading that treats "line bundles" might provide some illumination of _that_ general idea. In fact, you should read about "vector bundles", to better understand the simplest case, "line bundles". Sources on algebraic geometry, even "just" analytic geometry, such as Griffiths-Harris, discuss vector bundles (and line bundles) at great length. Looking at such sources you will see that, in the basic complex-analytic context, saying "line bundle" adds little to the discussion of modular forms.2012-09-25

0 Answers 0