Geodesic
Complete intersections of quadrics and complete intersections on Segre varieties with common specializations
Documenta mathematica, Tome 26 (2021), pp. 439-464.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We investigate whether surfaces that are complete intersections of quadrics and complete intersection surfaces in the Segre embedded product $\mathbf{P}^1\times \mathbf{P}^k\hookrightarrow \mathbf{P}^{2k+1}$ can belong to the same Hilbert scheme. For $k=2$ there is a classical example; it comes from K3 surfaces in projective $5$-space that degenerate into a hypersurface on the Segre threefold. We show that for $k\geq 3$ there is only one more example. It turns out that its (connected) Hilbert scheme has at least two irreducible components. We investigate the corresponding local moduli problem.
Classification : 14C05, 14J10, 14J25
Keywords: complete intersections of quadrics, Segre varieties, Hilbert schemes, local moduli 
@article{DOCMA_2021__26__a46,
     author = {Peters, Chris and Sterk, Hans},
     title = {Complete intersections of quadrics and complete intersections on {Segre} varieties with common specializations},
     journal = {Documenta mathematica},
     pages = {439--464},
     publisher = {mathdoc},
     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a46/}
}
TY  - JOUR
AU  - Peters, Chris
AU  - Sterk, Hans
TI  - Complete intersections of quadrics and complete intersections on Segre varieties with common specializations
JO  - Documenta mathematica
PY  - 2021
SP  - 439
EP  - 464
VL  - 26
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a46/
LA  - en
ID  - DOCMA_2021__26__a46
ER  - 
%0 Journal Article
%A Peters, Chris
%A Sterk, Hans
%T Complete intersections of quadrics and complete intersections on Segre varieties with common specializations
%J Documenta mathematica
%D 2021
%P 439-464
%V 26
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a46/
%G en
%F DOCMA_2021__26__a46
Peters, Chris; Sterk, Hans. Complete intersections of quadrics and complete intersections on Segre varieties with common specializations. Documenta mathematica, Tome 26 (2021), pp. 439-464. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a46/