Slope Stability for Lines on Products of Fano Manifolds

T. Suzuki

Utsunomiya University

Abstract: In this paper, we consider the slope stability of products $X$ of two Fano manifolds with Picard number 1 which are covered by lines. We show that such manifolds $X$ are slope stable with respect to lines for any polarization except $X=\mathbb P^1\times \mathbb P^{n-1}$.

Keywords: slope stability, Fano manifolds, covered by lines, Seshadri constant.

UDC: 512.77

Received: 28.12.2016

DOI: 10.4213/mzm12007

 English version: Mathematical Notes, 2018, 103:6, 968–976

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