arXiv Open Access 2002

The Frobenius map, rank 2 vector bundles and Kummer's quartic surface in characteristic 2 and 3

Yves Laszlo Christian Pauly

Lihat Sumber

Abstrak

Let X be a smooth projective curve of genus g>1 defined over an algebraically closed field k of characteristic p>0. Let M_X(r) be the moduli space of semi-stable rank r vector bundles with fixed trivial determinant. The relative Frobenius map F : X \to X_1 induces by pull-back a rational map V: M_{X_1}(r) \to M_X(r). We determine the equations of V in the following two cases (1) (g,r,p) = (2,2,2) and X non-ordinary with Hasse-Witt invariant equal to 1 (see math.AG/0005044 for the case X ordinary), and (2) (g,r,p) = (2,2,3). We also show, for any triple (g,r,p), the existence of base points of V, i.e., semi-stable bundles E such that F^* E is not semi-stable.

Topik & Kata Kunci

math.AG

Penulis (2)

Yves Laszlo

Christian Pauly

Format Sitasi

APA MLA BibTeX

Laszlo, Y., Pauly, C. (2002). The Frobenius map, rank 2 vector bundles and Kummer's quartic surface in characteristic 2 and 3. https://arxiv.org/abs/math/0203175

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2002
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓