The first of a two-part volume, this collection offers a unifying vision of algebraic geometry, exploring its evolution over the last four decades as well as state-of-the art research. With chapters written by established leaders in the field as well as younger researchers, readers will gain a wide-ranging perspective of the area. The volume also commemorates the significant talent and contributions of Alberto Collino, whose scientific accomplishments helped shape the themes and topics covered. Perspectives on Four Decades of Algebraic Geometry, Volume 1 will be a valuable resource for those interested in the ways algebraic geometry has expanded over the years and continues to grow.

"Quadratic Counts of Twisted Cubics" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Offers a unified vision of algebraic geometry, exploring its evolution as well as state-of-the art research Commemorates the significant talent and contributions of Alberto Collino, whose impact helped shape the field Features established leaders in the area as well as younger researchers, providing a wide range of perspectives

Inhalt

Singularities of bridgeland moduli spaces for k3 categories: an update.- On rigid manifolds of kodaira dimension 1.- On the components of the main stream of the moduli space of surfaces of general type with pg = q = 2.- Degree of irrationality of fano threefold hypersurfaces.- Non effective planar linear systems at the boundary of the mori cone.- Sur l'injectivite de l'application cycle de jannsen.- A prym hypergeometric.- Complete curves in the moduli space of polarized k3 surfaces and hyper-kahler manifolds.- The grothendieck group of algebraic stacks.- Conformal blocks in genus zero and the kz connection.- Second fundamental form and higher gaussian maps.- On infinitesimal invariants of normal functions.- Macaulay duality and its geometry.- On the chow ring of fano fourfolds of k3 type.- Quadratic counts of twisted cubics.