Limiting mixed Hodge structures associated to I-surfaces with simple elliptic singularities
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917859250143232 |
|---|---|
| author | Friedman, Robert Griffiths, Phillip |
| author_facet | Friedman, Robert Griffiths, Phillip |
| contents | An I-surface $X$ is a surface of general type with $K_X^2 =1$ and $p_g(X) =2$. This paper studies the asymptotic behavior of the period map for I-surfaces acquiring simple elliptic singularities. First we describe the relationship between the deformation theory of such surfaces and their $d$-semistable models. Next we analyze the mixed Hodge structures on the $d$-semistable models, the corresponding limiting mixed Hodge structures, and the monodromy. There are $6$ possible boundary strata for which the relevant limiting mixed Hodge structures satisfy: $\dim W_1 = 4$, and hence $W_2/W_1$ is of pure type $(1,1)$. We show that, in each case, the nilpotent orbit of limiting mixed Hodge structures determines the boundary stratum and prove a global Torelli theorem for one such stratum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02062 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limiting mixed Hodge structures associated to I-surfaces with simple elliptic singularities Friedman, Robert Griffiths, Phillip Algebraic Geometry 14J29, 14C34 (Primary) 14C30, 14D07 (Secondary) An I-surface $X$ is a surface of general type with $K_X^2 =1$ and $p_g(X) =2$. This paper studies the asymptotic behavior of the period map for I-surfaces acquiring simple elliptic singularities. First we describe the relationship between the deformation theory of such surfaces and their $d$-semistable models. Next we analyze the mixed Hodge structures on the $d$-semistable models, the corresponding limiting mixed Hodge structures, and the monodromy. There are $6$ possible boundary strata for which the relevant limiting mixed Hodge structures satisfy: $\dim W_1 = 4$, and hence $W_2/W_1$ is of pure type $(1,1)$. We show that, in each case, the nilpotent orbit of limiting mixed Hodge structures determines the boundary stratum and prove a global Torelli theorem for one such stratum. |
| title | Limiting mixed Hodge structures associated to I-surfaces with simple elliptic singularities |
| topic | Algebraic Geometry 14J29, 14C34 (Primary) 14C30, 14D07 (Secondary) |
| url | https://arxiv.org/abs/2408.02062 |