On Hodge level of weighted complete intersections of general type
Victor Przyjalkowski
TL;DR
This paper proves that smooth, well-formed weighted complete intersections of Cartier divisors of general type have maximal Hodge level, while this property does not extend to quasi-smooth cases.
Contribution
It establishes the maximal Hodge level property for smooth weighted complete intersections of Cartier divisors of general type, clarifying differences with quasi-smooth cases.
Findings
Smooth well-formed weighted complete intersections of Cartier divisors have maximal Hodge level.
The maximal Hodge level property does not hold for quasi-smooth cases.
Rightmost middle Hodge numbers do not vanish in the smooth case.
Abstract
We show that smooth varieties of general type which are well formed weighted complete intersections of Cartier divisors have maximal Hodge level, that is, their the rightmost middle Hodge numbers do not vanish. We show that this does not hold in the quasi-smooth case.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology