Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book
covers the standard topics in toric geometry; a novel feature is that each of the first nine …

Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate
relationship between Sasakian and Kähler geometries, especially when the Kähler structure …

We calculate the E-polynomials of certain twisted GL (n, ℂ)-character varieties M_n of
Riemann surfaces by counting points over finite fields using the character table of the finite …

We provide a complete description of normal affine varieties with effective algebraic torus
action in terms of what we call proper polyhedral divisors on semiprojective varieties. Our …

We define and study category $\mathcal O $ for a symplectic resolution, generalizing the
classical BGG category $\mathcal O $, which is associated with the Springer resolution. This …

We study the space of L^2 harmonic forms on complete manifolds with metrics of fibred
boundary or fibred cusp type. These metrics generalize the geometric structures at infinity of …

Abstract The BKMP conjecture (2006–2008) proposed a new method to compute closed and
open Gromov–Witten invariants for every toric Calabi–Yau 3-folds, through a topological …

We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric
geometry, we work with modules over a polynomial ring graded by a finitely generated …

We show that the equivariant Chow cohomology ring of a toric variety is naturally isomorphic
to the ring of integral piecewise polynomial functions on the associated fan. This gives a …

We present a new integration formula for intersection numbers on toric quotients, extending
the results of Witten, Jeffrey and Kirwan on localization. Our work was motivated by the Toric …