On the Space of Conics on Complete Intersections
Hong R. Zong
TL;DR
This paper establishes precise degree bounds ensuring the generic smoothness and connectedness of the space of conics on low degree complete intersections, extending classical results about lines on hypersurfaces.
Contribution
It provides new sharp degree bounds for the space of conics on complete intersections, generalizing previous work on Fano schemes of lines.
Findings
Sharp degree bounds for smoothness of conic spaces
Connectedness results for conic spaces on complete intersections
Extension of classical Fano scheme results
Abstract
We get sharp degree bound for generic smoothness and connectedness of the space of conics in low degree complete intersections which generalizes the old work about Fano scheme of lines on Hypersurfaces.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Advanced Numerical Analysis Techniques