Existence of Ulrich Bundle on general Surfaces

preprint2022arXivOpen access

Abstract

Let XX be a smooth projective algebraic surface of Picard rank one with very ample canonical bundle KXK_X. We further assume that q−1≤χ(OXq -1 \le χ(\mathcal{O}_X. In this article, we will study the existence of the Ulrich bundle and its stability property of it with respect to KXK_X.

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