Lines, conics, and all that
Ciro Ciliberto, Mikhail Zaidenberg
TL;DR
This survey reviews the properties and structures of Fano schemes of various algebraic curves and linear spaces within different classes of smooth projective varieties, highlighting recent developments and open questions.
Contribution
It provides a comprehensive overview of the current state of research on Fano schemes in various geometric contexts, synthesizing known results and identifying future directions.
Findings
Summarizes key properties of Fano schemes in different varieties.
Highlights recent advances in understanding the geometry of these schemes.
Identifies open problems and potential research avenues.
Abstract
This is a survey on the Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, etc.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Geometry and complex manifolds