Threefolds of order one in the six-quadric

Lev Borisov; Jeff Viaclovsky

doi:10.1134/S0081543809010039

Threefolds of order one in the six-quadric

Lev Borisov, Jeff Viaclovsky

Research output: Contribution to journal › Article › peer-review

Abstract

Consider the smooth quadric Q₆ in ℙ⁷. The middle homology group H ₆(Q ₆, ℤ) is isomorphic to double struck Z sign ⊕ double struck Z sign, with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree (1, p) inside Q ₆.

Original language	English (US)
Pages (from-to)	18-29
Number of pages	12
Journal	Proceedings of the Steklov Institute of Mathematics
Volume	264
Issue number	1
DOIs	https://doi.org/10.1134/S0081543809010039
State	Published - Apr 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.1134/S0081543809010039

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title = "Threefolds of order one in the six-quadric",

abstract = "Consider the smooth quadric Q6 in ℙ7. The middle homology group H 6(Q 6, ℤ) is isomorphic to double struck Z sign ⊕ double struck Z sign, with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree (1, p) inside Q 6.",

author = "Lev Borisov and Jeff Viaclovsky",

note = "Funding Information: Lev Borisov has been partially supported by the National Science Foundation, project no. DMS-0758480. Jeff Viaclovsky has been partially supported by the National Science Foundation, project no. DMS-0804042.",

year = "2009",

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doi = "10.1134/S0081543809010039",

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N2 - Consider the smooth quadric Q6 in ℙ7. The middle homology group H 6(Q 6, ℤ) is isomorphic to double struck Z sign ⊕ double struck Z sign, with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree (1, p) inside Q 6.

AB - Consider the smooth quadric Q6 in ℙ7. The middle homology group H 6(Q 6, ℤ) is isomorphic to double struck Z sign ⊕ double struck Z sign, with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree (1, p) inside Q 6.

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Threefolds of order one in the six-quadric

Abstract

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