Enumerative aspects of the Gross-Siebert program

Garrel, Michel van; Peter, Overholser, D.; Ruddat, Helge

doi:10.48550/arxiv.1410.4783

Cited by 1 publication

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This section aims to provide the reader with the background needed to study the Gross-Siebert approach to mirror symmetry, which will be discussed briefly in the final section of this survey (Sect. 5) and in significantly more detail in [32].…”

Section: Introductionmentioning

confidence: 93%

“…In [32], van Garrel, Overholser and Ruddat give an introduction to the program of Gross-Siebert, the main aim of which is to study mirror symmetry via toric degenerations. A toric degeneration is in some ways more specific and in other ways more general than a normal crossing degeneration.…”

Section: Hodge Theory Of Toric Degenerationsmentioning

confidence: 99%

“…This means that we don't know how to obtain the filtration W Y i , as we don't have a suitable replacement for Ω i X . Instead, to deal with log-differential forms on singular spaces, one uses logarithmic geometry; see [32].…”

Section: Hodge Theory Of Toric Degenerationsmentioning

confidence: 99%

“…With this definition, the sequence ( 4) is still exact in our setting. Let (B, P) denote the dual intersection complex of this toric degeneration, as defined in [32]. and it can be checked that the connecting homomorphism in cohomology…”

Section: Hodge Theory Of Toric Degenerationsmentioning

confidence: 99%

See 3 more Smart Citations

An Introduction to Hodge Structures

Filippini

Ruddat

Thompson

2015

Fields Institute Monographs

Self Cite

View full text Add to dashboard Cite

Abstract. We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kähler manifolds to the families of Hodge structures defined on their cohomology, and discuss its properties. This will lead us to the more general definition of a variation of Hodge structure and the Gauss-Manin connection. We then review the basics about mixed Hodge structures with a view towards degenerations of Hodge structures; including the canonical extension of a vector bundle with connection, Schmid's limiting mixed Hodge structure and Steenbrink's work in the geometric setting. Finally, we give an outlook about Hodge theory in the Gross-Siebert program.

show abstract

Section: Introductionmentioning

confidence: 93%

Section: Hodge Theory Of Toric Degenerationsmentioning

confidence: 99%

Section: Hodge Theory Of Toric Degenerationsmentioning

confidence: 99%

Section: Hodge Theory Of Toric Degenerationsmentioning

confidence: 99%

See 2 more Smart Citations