Introduces Bridgeland-Enriques general K3 surfaces whose degree-10 family detects categorical degeneration of special Gushel-Mukai threefolds and whose higher-degree families relate to Hodge-special Gushel-Mukai fourfolds and double EPW sextics.
EPW varieties as moduli spaces on ordinary GM surfaces and special GM threefolds
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abstract
We show that the double dual EPW sextic associated with a strongly smooth Gushel-Mukai surface can be realized as a moduli space of semistable objects on its bounded derived category. Also, we observe that the double dual EPW surface associated with a special Gushel--Mukai threefold can be realized as a moduli space of semistable objects on its Kuznetsov component. Then we discuss extensions of our main results to double EPW sextics and double EPW surfaces and a refinement of a statement of Bayer and Perry about Gushel-Mukai threefolds with equivalent Kuznetsov components, under a mild assumption.
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math.AG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Bridgeland-Enriques general K3 surfaces
Introduces Bridgeland-Enriques general K3 surfaces whose degree-10 family detects categorical degeneration of special Gushel-Mukai threefolds and whose higher-degree families relate to Hodge-special Gushel-Mukai fourfolds and double EPW sextics.