On the Dimension and Degree of the Projective Dual Variety: A q-Analog of the Katz-Kleiman Formula

I. M. Gelfand and M. M. Kapranov ()
Additional contact information
I. M. Gelfand: Rutgers University, Department of Mathematics
M. M. Kapranov: Rutgers University, Department of Mathematics

A chapter in The Gelfand Mathematical Seminars, 1990–1992, 1993, pp 27-33 from Springer

Abstract: Abstract Let X ⊂ P N be a complex projective variety. Let $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}\to {P} ^N$$ be the projective space whose points are hyperplanes in P N . Let x ∈ X be any smooth point. A hyperplane $$H \in \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}\to {P} ^N$$ is said to be tangent to X at x if H contains the tangent subspace T xX. The projective dual variety $$X^V \subset \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}\to {P} ^N$$ is defined as the closure of the locus of those hyperplanes H which are tangent to X in some smooth point, see [7]. The name “projective dual” is justified by the biduality theorem [7]: the dual to X⋁ coincides with X.

Keywords: Chern Class; Cohomology Ring; Smooth Point; Coherent Sheave; Coherent Sheaf (search for similar items in EconPapers)
Date: 1993
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0345-2_4

Ordering information: This item can be ordered from
http://www.springer.com/9781461203452

DOI: 10.1007/978-1-4612-0345-2_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().