Details
| Original language | English |
|---|---|
| Pages (from-to) | 295-342 |
| Number of pages | 48 |
| Journal | Geometry and Topology |
| Volume | 19 |
| Issue number | 1 |
| Publication status | Published - 27 Feb 2015 |
| Externally published | Yes |
Abstract
Keywords
- Construction problem, Kähler geometry, Hodge numbers
ASJC Scopus subject areas
- Mathematics(all)
- Geometry and Topology
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In: Geometry and Topology, Vol. 19, No. 1, 27.02.2015, p. 295-342.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the construction problem for Hodge numbers
AU - Schreieder, Stefan
PY - 2015/2/27
Y1 - 2015/2/27
N2 - For any symmetric collection (hp,q)p+q=k of natural numbers, we construct a smooth complex projective variety X whose weight-k Hodge structure has Hodge numbers hp,q(X)= hp,q; if k D 2m is even, then we have to impose that hm,m is bigger than some quadratic bound in m. Combining these results for different weights, we solve the construction problem for the truncated Hodge diamond under two additional assumptions. Our results lead to a complete classification of all nontrivial dominations among Hodge numbers of Kähler manifolds.
AB - For any symmetric collection (hp,q)p+q=k of natural numbers, we construct a smooth complex projective variety X whose weight-k Hodge structure has Hodge numbers hp,q(X)= hp,q; if k D 2m is even, then we have to impose that hm,m is bigger than some quadratic bound in m. Combining these results for different weights, we solve the construction problem for the truncated Hodge diamond under two additional assumptions. Our results lead to a complete classification of all nontrivial dominations among Hodge numbers of Kähler manifolds.
KW - Construction problem
KW - Kähler geometry
KW - Hodge numbers
UR - http://www.scopus.com/inward/record.url?scp=84924287328&partnerID=8YFLogxK
U2 - 10.2140/gt.2015.19.295
DO - 10.2140/gt.2015.19.295
M3 - Article
AN - SCOPUS:84924287328
VL - 19
SP - 295
EP - 342
JO - Geometry and Topology
JF - Geometry and Topology
SN - 1465-3060
IS - 1
ER -