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

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We investigate whether surfaces that are complete intersections of quadrics and complete intersection surfaces in the Segre embedded product P1×Pk↪P2k+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≥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.
DOI : 10.4171/dm/818
Classification : 14C05, 14J10, 14J25
Mots-clés : complete intersections of quadrics, Segre varieties, Hilbert schemes, local moduli 
Hans Sterk; Chris Peters. Complete intersections of quadrics and complete intersections on Segre varieties with common specializations. Documenta mathematica, Tome 26 (2021), pp. 439-464. doi: 10.4171/dm/818
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     author = {Hans Sterk and Chris Peters},
     title = {Complete intersections of quadrics and complete intersections on {Segre} varieties with common specializations},
     journal = {Documenta mathematica},
     pages = {439--464},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/818},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/818/}
}
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