English

Numerical inequalities for quasi-projective surfaces

Algebraic Geometry 2026-03-31 v1

Abstract

Let VV be a smooth quasi-projective complex surface with compactification (X,D)(X,D) and set P1(V):=h0(X,KX+D)\overline P_1(V):=h^0(X,K_X+D), q(V):=h0(X,ΩX1(logD))\overline q(V):=h^0(X,\Omega^1_X(\log D)). We prove that P1(V)q(V)1\overline P_1(V)\ge \overline q(V)-1 if VV has maximal Albanese dimension and P1(V)16(q(V)5)\overline P_1(V)\ge\frac 16( \overline q(V)-5) otherwise. Both bounds are sharp.

Keywords

Cite

@article{arxiv.2603.27596,
  title  = {Numerical inequalities for quasi-projective surfaces},
  author = {Rita Pardini and Sofia Tirabassi},
  journal= {arXiv preprint arXiv:2603.27596},
  year   = {2026}
}

Comments

12 pages, comments are welcome

R2 v1 2026-07-01T11:42:45.981Z