By Carel Faber, Gerard van der Geer, Eduard Looijenga

Attention-grabbing and remarkable advancements are occurring within the class of algebraic kinds. The paintings of Hacon and McKernan etc is inflicting a wave of breakthroughs within the minimum version software: we now recognize that for a gentle projective style the canonical ring is finitely generated. those new effects and strategies are reshaping the sphere. encouraged through this interesting growth, the editors prepared a gathering at Schiermonnikoog and invited top specialists to write down papers in regards to the contemporary advancements. the result's the current quantity, a full of life testimony to the unexpected advances that originate from those new principles. This quantity can be of curiosity to a variety of natural mathematicians, yet will attraction specially to algebraic and analytic geometers. A ebook of the eu Mathematical Society (EMS). dispensed in the Americas by means of the yank Mathematical Society.