Intersection theory of nef<i>b</i>-divisor classes

Intersection Theory Classes 20 and 21: Bivariant Intersection Theory

Characteristic Classes, Chern Classes and Applications to Intersection Theory

This is a report for my summer REU program at the University of Chicago, 2014. I would like to acknowledge my mentor Sean Howe in this program for his generous guidance on learning the subject and writing this article, Professor J.P. May who runs this REU program successfully and made my wonderful experience possible, and Professor M. Yan who has encouraged me ever since my first year in colleg...

Rational Divisors in Rational Divisor Classes

We discuss the situation where a curve C, defined over a number field K, has a known K-rational divisor class of degree 1, and consider whether this class contains an actual K-rational divisor. When C has points everywhere locally, the local to global principle of the Brauer group gives the existence of such a divisor. In this situation, we give an alternative, more down to earth, approach, whi...

Effective Divisor Classes on a Ruled Surface

The Neron-Severi group of divisor classes modulo algebraic equivalence on a smooth algebraic surface is often not difficult to calculate, and has classically been studied as one of the fundamental invariants of the surface. A more difficult problem is the determination of those divisor classes which can be represented by effective divisors; these divisor classes form a monoid contained in the N...

Positivity of Divisor Classes on the Strata of Differentials

Three decades ago Cornalba-Harris proved a fundamental positivity result for divisor classes associated to families of stable curves. In this paper we establish an analogous positivity result for divisor classes associated to families of stable differentials.