English

On singularities of ${\cal M}_{I\!\! P^3}(c_1,c_2)$

alg-geom 2015-06-30 v1 Algebraic Geometry

Abstract

Let MI ⁣ ⁣P3(c1,c2){\cal M}_{I\!\! P^3}(c_1,c_2) be the moduli space of stable rank-22 vector bundles on I ⁣ ⁣P3I\!\! P^3 with Chern classes c1c_1, c2 c_2. We prove the following results. 1) Let 0β<γ0 \le \beta < \gamma be two integers, (γ2)\gamma \ge 2), such that 2γ3β>02\gamma-3\beta>0; then MI ⁣ ⁣P3(0,2γ23β2){\cal M}_{I\!\! P^3}(0,2\gamma^2-3\beta^2) is singular (the case β=0\beta =0 was previously proved by M. Maggesi). 2) Let 0β<γ0 \le \beta < \gamma be two odd integers (γ5)\gamma \ge 5), such that 2γ3β+1>02\gamma-3\beta+1>0; then MI ⁣ ⁣P3(1,2(γ/2)23(β/2)2+1/4){\cal M}_{I\!\! P^3}(-1,2(\gamma/2)^2-3(\beta/2)^2+1/4) is singular. In particular MI ⁣ ⁣P3(0,5){\cal M}_{I\!\! P^3}(0,5), MI ⁣ ⁣P3(1,6){\cal M}_{I\!\! P^3}(-1,6) are singular.

Keywords

Cite

@article{arxiv.alg-geom/9502008,
  title  = {On singularities of ${\cal M}_{I\!\! P^3}(c_1,c_2)$},
  author = {Vincenzo Ancona and Giorgio Ottaviani},
  journal= {arXiv preprint arXiv:alg-geom/9502008},
  year   = {2015}
}

Comments

7 pages, Plain Tex