AT THE CENTER of the international financial meetings here over the coming week are the Latin American debts. Brazil wants sweeping write-offs and has given a certain urgency to its demands by refusing for the past seven months to pay interest on $68 billion in loans from commercial banks. The money men are now beginning to gather -- finance ministers, bankers, lenders and borrowers from nearly every country on earth, in their long black limousines. One question is what's fair to Brazil and to its creditors. Another question is what's possible.

The occasion is the annual joint meeting of the International Monetary Fund, whose main business is financial stability, and the World Bank, whose main business is economic development. That's what the Brazilian case is about -- stability of a world financial system now in peril of a gigantic default, and the development of Brazil and the dozen or so other major debtors for whom Brazil is likely to set the precedent.

The Brazilian position is that, since the rest of the world has cut down new lending to Brazil, full repayment is no longer possible. The Reagan administration, and most of the other creditor countries along with it, are now responding by saying that if Brazil deals in good faith with them, new money will indeed be available.

Paul Volcker, the former chairman of the Federal Reserve Board, speaking Wednesday in New York, laid out a view that seems to be widely shared among the rich countries. Write-downs, he said, are unworkable. Among other malign effects, they would lead to less trade credit for Brazil and threaten growth there. What's needed, he said, is a renewed cooperative effort. The big debtors are capable of carrying their present debts, and even somewhat more. But to finance the investment that growth requires, they are going to need "significant amounts" of new lending.

James A. Baker, the secretary of the Treasury, said on the same day that the administration supports a substantial increase in the World Bank's lending authority. He gave no figures, but he seems to have in mind something upward of $40 billion -- that is, an increase by half or more in the bank's present size. The chief purpose is to expand the flow of credit to the debtor countries.

In return, the rich countries want assurances of economic reform. Above all, the rich countries want assurance that Latin America intends to stay in the international trading system and keep its markets relatively open, rather than retreating, as it has done before, into protection and the kind of inefficiency that is highly profitable for a few well-connected people.

The rich countries acknowledge one more responsibility. They have to keep up economic growth rates in their part of the world, to ensure hungry markets for Latin exports. Everything else depends on that.

The word is that nothing very dramatic will happen in the coming week's meetings. That wouldn't necessarily be a bad sign. Breakdowns are dramatic; the patient work of holding things together is not