The objective is to show the construction of an Ulrich vector bundle on the blowing-up Y of a nonsingular projective variety X at a closed point, where the original variety is embedded by a very ample divisor H and carries an Ulrich vector bundle. In order to achieve this result, we aim to find a suitable very ample divisor on Y , which is dependent on H. At the end, we take into consideration some applications to surfaces with regards to minimal models and their Kodaira dimension.
On the existence of Ulrich bundles on blown-up varieties at a point
Secci S. A.
2019-01-01
Abstract
The objective is to show the construction of an Ulrich vector bundle on the blowing-up Y of a nonsingular projective variety X at a closed point, where the original variety is embedded by a very ample divisor H and carries an Ulrich vector bundle. In order to achieve this result, we aim to find a suitable very ample divisor on Y , which is dependent on H. At the end, we take into consideration some applications to surfaces with regards to minimal models and their Kodaira dimension.
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