Singularities of metrics on Hodge bundles and their topological invariants

• We consider degenerations of complex projective Calabi-Yau varieties and study the singularities of L2, Quillen and BCOV metrics on Hodge and determinant bundles. The dominant and subdominant terms in the expansions of the metrics close to non-smooth fibers are shown to be related to well-known topological invariants of singularities, such as limit Hodge structures, vanishing cycles and log-canonical thresholds. We also describe corresponding invariants for more general degenerating families in the case of the Quillen metric.

Ämnesord

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Log-canonical threshold

Vanishing cycle

Milnor number

Quillen metric

L -metric 2

BCOV metric

Degeneracy index

Hodge bundles

Limit Hodge structure

BCOV metric

Degeneracy index

Hodge bundles

L2-metric

Limit Hodge structure

Log-canonical threshold

Milnor number

Quillen metric

Vanishing cycle

Publikations- och innehållstyp

art (ämneskategori)

ref (ämneskategori)