Positivity of double point divisors
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912141950320640 |
|---|---|
| author | Cho, Yonghwa Park, Jinhyung |
| author_facet | Cho, Yonghwa Park, Jinhyung |
| contents | The non-isomorphic locus of a general projection from an embedded smooth projective variety to a hypersurface moves in a linear system of an effective divisor which we call the double point divisor. David Mumford proved that the double point divisor from outer projection is always base point free, and Bo Ilic proved that it is ample except for a Roth variety. The first aim of this paper is to show that the double point divisor from outer projection is very ample except in the Roth case. This answers a question of Bo Ilic. Unlike the case of outer projection, the double point divisor from inner projection may not be base point free nor ample. However, Atsushi Noma proved that it is semiample except when a variety is neither a Roth variety, a scroll over a curve, nor the second Veronese surface. In this paper, we investigate when the double point divisor from inner projection is base point free or big. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positivity of double point divisors Cho, Yonghwa Park, Jinhyung Algebraic Geometry 14N05, 14E25 The non-isomorphic locus of a general projection from an embedded smooth projective variety to a hypersurface moves in a linear system of an effective divisor which we call the double point divisor. David Mumford proved that the double point divisor from outer projection is always base point free, and Bo Ilic proved that it is ample except for a Roth variety. The first aim of this paper is to show that the double point divisor from outer projection is very ample except in the Roth case. This answers a question of Bo Ilic. Unlike the case of outer projection, the double point divisor from inner projection may not be base point free nor ample. However, Atsushi Noma proved that it is semiample except when a variety is neither a Roth variety, a scroll over a curve, nor the second Veronese surface. In this paper, we investigate when the double point divisor from inner projection is base point free or big. |
| title | Positivity of double point divisors |
| topic | Algebraic Geometry 14N05, 14E25 |
| url | https://arxiv.org/abs/2412.02208 |