A new spinor modification construction relates conic bundles with equivalent kernel categories, yielding explicit derived category descriptions for 1-nodal Fano threefolds.
One-nodal Fano threefolds with Picard number one
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abstract
We classify all 1-nodal degenerations of smooth Fano threefolds with Picard number 1 (both nonfactorial and factorial) and describe their geometry. In particular, we describe a relation between such degenerations and smooth Fano threefolds of higher Picard rank and with unprojections of complete intersection varieties.
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Spinor modifications of conic bundles and derived categories of 1-nodal Fano threefolds
A new spinor modification construction relates conic bundles with equivalent kernel categories, yielding explicit derived category descriptions for 1-nodal Fano threefolds.